QA – Placement Quizzes | Permutation and Combination | Question 7

In how many ways can 20 boys and 18 girls make a queue such that no two girls are together?
(A) 20!* ²⁰C₁₈
(B) 20!* ²⁰P₁₈
(C) 20!* ²¹C₁₈
(D) 20!* ²¹P₁₈


Answer: (D)

Explanation: The boys will be arranged in 20! ways. Now, there are a total of 21 possible places available between boys such that no 2 girls can be placed together (alternate sequence of boys and girls, starting and ending positions for girls).
Therefore, the 18 girls can stand at these 21 places only.
Hence, the number of ways = 20!* ²¹P₁₈
Option (D) is correct.

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