Permutation and CombinationEasy
Question
Consider a photo session of 3 teachers, 6 boys and 5 girls in a line such that no two teachers are together, boys stand in increasing order of their height and girls in decreasing order of their height.
If number of such arrangements is k.22.11C5, then ′k′ is divisible by (Assume all students to be of different heights) -
If number of such arrangements is k.22.11C5, then ′k′ is divisible by (Assume all students to be of different heights) -
Options
A.8
B.10
C.12
D.15
Solution
First select 6 places out of 11 for the boys in 11C6 ways. Number of ways of arrangement at these places = 1 & at the remaining 5 places girls can stand in the way. Now there are 12 gaps & teachers can be arranged in 12P3 ways
∴ total ways = 12P3 × 11C6
= 12 × 11 × 10 × 11C6
= 22 × 11C6 × 60
⇒ k = 60
∴ total ways = 12P3 × 11C6
= 12 × 11 × 10 × 11C6
= 22 × 11C6 × 60
⇒ k = 60
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