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Q. Let m denotes the number of ways in which 5 boys and 5 girls can be arranged in a line alternately and n denotes the number of of ways in which 5 boys and 5 girls can be arranged in a circle so that no two boys are together. If m = kn then the value of k is

Permutations and Combinations

Solution:

$m = 5! · 2 · 5! = 10 · 4! · 5! $
$n = 4! · 5!$
Hence $m =10 n \Rightarrow k =10$