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Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..

Question 21 - Question: A family of 4 brothers and 3 sisters is to be arranged in a row for a photograph. In how many ways can they be seated if all the sisters are together? Answer: Let B 1 ,B 2 ,B 3 ,B 4 denote the brothers and S 1 ,S 2 ,S 3 denote the sisters. Since the sisters are to be seated ..

Question 21 - Question: A letter lock consists of three rings, each marked with fifteen different letters. Find in how many ways it is possible to make an unsuccessful attempt to open the lock. Answer: 1 s t ring can be attempted in 15 ways. 1 s t and 2 n d ring can be attempted in 15 x 15 = 15 2 w..

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Question: Find n if P(n,4) = 20P(n,2) Answer: ..

Question: Answer: = 5 + 10 + 10 + 5 + 1 = 31 = RH..

Question: A candidate is required to answer 6 out of 10 questions, which are divided into two groups, each containing 5 questions, and he is not permitted to attempt more than 4 from each group. In how many ways can he make his choice? Answer: ..

Question: vi) (n! + 1) is not divisible by any natural number between 2 and n. vii) Simplify Answer: ..