Exercise :: Permutation and Combination  General Questions
 Permutation and Combination  Important Formulas
 Permutation and Combination  General Questions
1.  From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? 

Answer: Option D Explanation: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

2.  In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? 

Answer: Option C Explanation: The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720. 
3.  In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together? 

Answer: Option D Explanation: In the word 'CORPORATION', we treat the vowels OOAIO as one letter. Thus, we have CRPRTN (OOAIO). This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
Required number of ways = (2520 x 20) = 50400. 
4.  Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? 

Answer: Option C Explanation: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters.
Required number of ways = (210 x 120) = 25200. 
5.  In how many ways can the letters of the word 'LEADER' be arranged? 

Answer: Option C Explanation: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
