The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels not occur together is (a) 1200(b) 2400(c) 14400(d) none of these Show
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Hint: In this question, we first need to find the total number of arrangements possible with the given letters of the word using the permutation formula given by \[{}^{n}{{P}_{r}}\]. Then we need to find the number of words in which two vowels are together but first selecting the two vowels and then arranging all the letters using the formula \[{}^{n}{{C}_{r}}\]. Now, find the number of words in which 3 vowels are together and then subtract 2 vowels together from total words and add 3
vowels together.Complete step by step solution: Note: No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! Solution The correct option is C14400The explanation for the correct answer.Find the number of ways such that no two vowels occur together.Given: TRIANGLEThe total number of letters in the word triangle is 8.The total number of words that can be formed =8!=40320.The total number of words in which two vowels occur together =C2×7!×2!= 302403.The number of ways where all vowels occur together =C3×6!×3!= 43203.Therefore required number of words =40320-30240+4320=14400.Hence option (C) is the correct answer.Textbooks Question Papers Home How many of them have arrangements that no two vowels are together in TRIANGLE?Hence, the number of arrangements of the letters of the word TRIANGLE in which no two of the vowels are adjacent is 5!
How many vowels are in TRIANGLE?... triangle consists of the three vowels /a/, /i/ and /u/ represented in the space of the two first for- mant frequencies F 1 and F 2 (here estimated via Wavesurfer [10]). For the three degrees of articulation, the vocalic triangle is displayed in Figure 1 for the original sentences.
How many different words can be formed with the letters of the word TRIANGLE having no two vowels together?3 ! Here, the required arrangement = 14400 ways.
How many words can be formed from the letters of the word TRIANGLE so that vowels always come together?720`. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
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