How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

Given:

5, 6, 7, 8, 9 are the digits to form 3 digit number

Calculation:

Let us take the 3digit number as H T U (Hundreds, tens, unit digit)  respectively

To make 3 digit number as odd

5, 7, 9 are only possibly be used in the unit digit place

In hundreds and tens place all  5 digits are possible 

Number of ways for unit digit = 3

Number of ways for tens digit = 5

Number of ways for hundreds digit = 5

Number of 3 digits odd number =  3 × 5 × 5 = 75 

∴ 75 Three-digit odd numbers can be formed from the digits 5, 6, 7, 8, 9 if the digits can be repeated

Solution : For a number to be odd, we must have 1, 3 of 5 at the unit's palce. So, there are 3 ways of filling the unit's place. <br> Case (i) When the repetition of digits is not allowed: <br> In this case, after filling the unit's place, we may fill the ten's place by any of the remaining five digits. So, there are 5 ways of filling the ten's place. <br> Now, the hundred's place can be filled by any of the remaining 4 digits. So, there are 4 ways of filling the hundred's place. <br> So, by the fundamental principle of multiplication, the required number of odd numbers `=(3xx5xx4) = 60.` <br> Case (ii) When the repetition of digits is allowed: <br> Since the repetition of digits is allowed, so after filling the unit's place, we may fill the ten's place by any of the given six digits. So, there are 6 ways of filling the ten's place. Similarly, the hundred's palce can be filled by any of the given six digits. So, it can be filled in 6 ways. <br> Hence, by the fundamental principle of multiplication, the required number of odd numbers `= (3xx6xx6) = 108.`

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed.


How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

Number of digits available = 5

Number of places for the digits = 3.

Number of ways in which place (x) can be filled = 5

                           m = 5

Number of ways in which place (y) can be filled = 5    (∵  Repetition is allowed)

                            n = 5

Number of ways in which place (z) can be filled = 5    (∵ Repetition is allowed)

                             p = 5

∴ By fundamental principle of counting, the number of 3-digit numbers formed.                           = m x n x p = 5 x 5 x 5 = 125

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Given 5 flags of different colours, how many different signals can be generated if each signal requires use of 2 flags, one below the other?


How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

Number of ways of finding a flag for place 1 = 5

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                           m = 5

Number of remaining flags = 4

Number of ways of finding a flag for place 2 to complete the signal = 4

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                     n = 4

∴ By fundamental principle of counting, the number of signals generated                       = 

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

991 Views


How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed.


Number of ways in which place (x) can be filled = 5

                                           m = 5

Number of ways in which place (y) can be filled = 4      (∵ Repetition is not allowed)

                                           n = 4

Number of ways in which place (z) can be filled = 3      (∵ Repetition is not allowed)

                                           p = 3

∴ By fundamental principle of counting, the total number of 3 digit numbers formed                                         = m x n x p = 5 x 4 x 3 = 60.

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How many 3-digit odd numbers can be formed from the digits 1,2,3,4,5,6 if:(a) the digits can be repeated (b) the digits cannot be repeated?


How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

(a) Number of digits available = 6

Number of places [(x), (y) and (z)] for them = 3

Repetition is allowed and the 3-digit numbers formed are odd

Number of ways in which box (x) can be filled = 3 (by 1, 3 or 5 as the numbers formed are to be odd)

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
               m = 3
Number of ways of filling box (y) = 6                           (∴ Repetition is allowed)

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
               n = 6

Number of ways of filling box (z) = 6                           (∵ Repetition is allowed)

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
              p = 6

∴  Total number of 3-digit odd numbers formed

                             = m x n x p = 3 x 6 x 6 = 108

(b) Number of ways of filling box (x) = 3                     (only odd numbers are to be in this box )

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                                   m = 3

Number of ways of filling box (y) = 5                                (∵ Repetition is not allowed)

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                              n = 5

Number of ways of filling box (z) = 4                                 (∵ Repetition is not allowed)

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                             p = 4

∴     Total number of 3-digit odd numbers formed

                                  = m x n x p = 3 x 5 x 4 = 60.

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A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?


           

Event 1: A coin is tossed and the outcomes recorded.

                                Number of outcomes 

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                                      m = 2

Event 2: The coin is tossed again and the outcomes recorded.

            Number of outcomes 

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                                       n = 2

Event 3: The coin is tossed third time and the outcomes recorded.

           Number of outcomes 

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?
                                           p = 2

∴  By fundamental principle of counting, the total number of outcomes recorded                                                     = 

How many three digit numbers can be formed from the digits 1,2 3 4 and 5 B How many different three digit odd numbers can be formed?

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How many 3 digits odd numbers can be formed from 4 digits 1,2 3 4 )? While I repetition not allowed II repetition allowed?

So there are 3 ways of filling the unit's place. As repetition of digits is not allowed, the ten's place can be filled in 5 ways with any of the remaining 5-digts and the hundred's place can be filled in 4 ways by the remaining 4-digits. So, Required number of three-digit odd numbers = 3 × 5 × 4 = 60.

How many 3

Hence, the number of 3-digit odd numbers that can be formed =3×6×6=108. Q.

How many 3

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed. = m x n x p = 5 x 4 x 3 = 60. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed. Number of places for the digits = 3.

How many 3

Problem 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated? Solution: Answer: 108. Let 3-digit number be XYZ.