 Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all coursesQ Prove that: Page 2Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation Q Prove that: Q: If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ‘X’ as the answer. If no such word can be formed, give ‘Z’ as the answer. Answer & Explanation Answer: D) R Explanation: The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ‘R’.
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In how many ways can the letters of the word ABACUS be rearranged [#permalink]
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Question Stats: Hide Show timer StatisticsIn how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together? A. 6!/2! B. 3!*3! C. 4!/2! D. 4! *3!/2! E. 3!*3!/2 _________________
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Re: In how many ways can the letters of the word ABACUS be rearranged [#permalink] ABACUS = AAU BCS = Let's say AAU is altogether one entityso we have 4 entities = (AAU)(BCS) = so 4 entities can be arranged in 4! ways and within them ( the group - AAU can be arranged in \(\frac{3!}{2!}\)) ways so total number of ways = 4! * \(\frac{3!}{2!}\) = 24 * \(\frac{6}{2}\) = 24 * 3 = 72
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Re: In how many ways can the letters of the word ABACUS be rearranged [#permalink] In the word ABACUS , there are 3 vowels - 2 A's and UNumber of ways the letters of word ABACUS be rearranged such that the vowels always appear together= (4! * 3! )/2!We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! .The entire vowel group is considered as a single group .Answer D _________________
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Re: In how many ways can the letters of the word ABACUS be rearranged [#permalink] Since the vowels, must always appear together(you combine the vowels as 1 unit) They can be arranged AUA, UAA and AAU(3 ways) such that vowels occur togther : 24*3 = 72(Option D) _________________
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Re: In how many ways can the letters of the word ABACUS be rearranged [#permalink]
Bunuel wrote: jokschmer wrote: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?a) 144b) 12c) 36d) 72 e) 81 Merging topics. Please refer to the solutions above. Considering vowels as a single unit. It would be like {AAU}{B}{C}{S} so number of arrangements for this would be 4! = 4*3*2*1 = 24 AND {AAU} consists of 3 letters so it can be arranged in 3! ways = 3*2*1 = 6 ways. So, total number of arrangements would be 4! * 3! = 24 * 6 = 144 ways.A is the answer.
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Re: In how many ways can the letters of the word ABACUS be rearranged [#permalink]
reachskishore wrote: Bunuel wrote: jokschmer wrote: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?a) 144b) 12c) 36d) 72 e) 81 Merging topics. Please refer to the solutions above. 3!/2!Considering vowels as a single unit. It would be like {AAU}{B}{C}{S} so number of arrangements for this would be 4! = 4*3*2*1 = 24 AND {AAU} consists of 3 letters so it can be arranged in 3! ways = 3*2*1 = 6 ways. So, total number of arrangements would be 4! * 3! = 24 * 6 = 144 ways. A is the answer. AAU has two identical letters, hence the ways of arranging them will be will be \(\frac{3!}{2!}\) or 3 ways _________________
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Re: In how many ways can the letters of the word ABACUS be rearranged [#permalink]
Bunuel wrote: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together? A. 6!/2! B. 3!*3! C. 4!/2! D. 4! *3!/2! E. 3!*3!/2 We can arrange the letters as follows:[A-A-U] - B - C - SThinking of [A-A-U] as a single element, [A-A-U] - B - C - S can be arranged in 4! ways. We must also consider that [A-A-U] can be arranged in 3!/2! ways (by the formula for permutations with indistinguishable objects).Thus, the total number of ways is 4! * 3!/2!. Answer: D _________________
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Re: In how many ways can the letters of the word ABACUS be rearranged [#permalink]
Bunuel wrote: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together? A. 6!/2! B. 3!*3! C. 4!/2! D. 4! *3!/2! E. 3!*3!/2 We need to arrange [A-A-U] - B - C - SSince A-A-U is considered one letter, the total arrangement can be arranged in 4! ways.A-A-U can be arranged in 3!/2! = 3 ways.So, the total number of ways to arrange the letters with the vowels together is 4! x 3!/2! ways.Answer: D _________________
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Re: Permutation and Combination [#permalink] 16 Jan 2021, 02:43 |
In how many ways can the letters of the word ABACUS be arranged so that all vowels come together
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