Exercise :: Permutation and Combination  General Questions
 Permutation and Combination  Important Formulas
 Permutation and Combination  General Questions
6.  In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? 

Answer: Option D Explanation: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

7.  How many 3digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated? 

Answer: Option D Explanation: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place. The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it. Required number of numbers = (1 x 5 x 4) = 20. 
8.  In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women? 

Answer: Option C Explanation:

9.  A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw? 

Answer: Option C Explanation: We may have(1 black and 2 nonblack) or (2 black and 1 nonblack) or (3 black).

10.  In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions? 

Answer: Option C Explanation: There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants. Let us mark these positions as under: (1) (2) (3) (4) (5) (6) Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5. Number of ways of arranging the vowels = ^{3}P_{3} = 3! = 6. Also, the 3 consonants can be arranged at the remaining 3 positions. Number of ways of these arrangements = ^{3}P_{3} = 3! = 6. Total number of ways = (6 x 6) = 36. 