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  4. There are 9 children comprising of 3 boys and 6 girls. Let m denotes the number of ways they can be seated in a line when all the 3 boys are in succession and n denotes the corresponding figure when the two end position are occupied by boys. If m = kn then k is equal to

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Q. There are 9 children comprising of 3 boys and 6 girls. Let m denotes the number of ways they can be seated in a line when all the 3 boys are in succession and n denotes the corresponding figure when the two end position are occupied by boys. If $m = kn$ then k is equal to

Permutations and Combinations

Solution:

$m = 3! ยท 7!$
image
$n ={ }^3 C _2 \cdot 2 ! 7 !=3 ! 7 !$
Hence $k = 1$