Video TranscriptIn this problem, first of all, we have been asked in how many ways can a 2 persons sub committee be selected from a committee of 9 people, so out of 9 people, any 2 need to be selected for the sub committee and the number of ways. This can be done is 9 c 2. Here we use c, which represents combination, and we use combination and not permutation in this case, because the order of selection of the people does not matter so. We just need to calculate this now recall that n c r is equal to n factorial by r factorial times n minus r factorial. So in this case we can see that the value of n is 9 and the value of r is 2 point. So we have 9 factorial by 2 factorial times a factorial of 9 minus 2, which is 7, and if we calculate this we will obtain 36 point. So the number of ways a 2 persons sub committee can be selected from a committee of 9. People is equal to 36 poi. Next, we have been asked in how many ways can a president and a vice president be chosen from a committee of 9 people? So we have 9 people and we need to select any 2 people for those 2 posts of president and vice president and the number of ways this can be done is 9 p 2. Here we use p, which represents per mutation, and we use permutation and not combination in this case, because the order of selection of the people matters, we consider the first person elected to be the president and the second person considered to be the vice selected to be The vice president, so the order of selection matters and we need to use for mutation so recall the formula for n p r, that is n factorial by n minus r factorial. So, in this case, n is 9 r is 2, so we have 9 factorial divided by the factorial of 9 minus 2, which is 7, and if we calculate this we will obtain 72 point. So the number of ways, a president and vice president can be chosen from a committee of 9 people is equal to 72 pi. Show
Natalia P. How many ways can a 2-person subcommittee be selected from a committee of 7 people? I need help with this problem please More 1 Expert Answer
Omari S. answered • 11/24/15 Johns Hopkins Grad Student and MCPS Math Teacher w/ Eng. Background Use the combination rule of n!/k!(n-k)! where n is the number of options (7) and k is the number of slots (2). Do this if the order does not matter. 7!/2!(7-2)! = 7*6*5*4*3*2*1/2*1*(5*4*3*2*1) = 7*6/2 = 21 If, however, the order does matter, then use the permutation rule of n!/(n-k!) with n = 7 and k =2 giving 7*6 = 42. Still looking for help? Get the right answer, fast.ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. How many ways can a 4 person subcommittee be selected from a committee of 7 people?A committee of 4 people be selected from a group of 7 people in 35 ways.
How many ways can a two person subcommittee be selected from a committee of nine people?So we have 9 factorial by 2 factorial times a factorial of 9 minus 2, which is 7, and if we calculate this we will obtain 36 point. So the number of ways a 2 persons sub committee can be selected from a committee of 9. People is equal to 36 poi.
How many ways can a be chosen from a committee of 8 people?=8×7×6! 6! =56.
How many ways are there to select a subcommittee of 3 members from among a committee of 10?Example 1.7. How many ways can one choose a committee of 3 out of 10 people? ) = 120.
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