Question

In a group of boys the number of arrangement of 4 boys is 12 times the number of arrangement of 2 boys.the number of boys in the group is

Answer 1

Answer:

Assume the number of boys to be 'n'

=> nP4 = 12 × nP2

nP4 = n ! / ( n - 4 ) !

nP2 = n ! / ( n - 2 ) !

This can also be written as:

nP4 = n ! ( n - 2 ) ( n - 3 ) ( n - 4 ) !

Substituting in the equation we get,

=> n ! ( n - 4 ) ! = 12 × n ! / ( n - 2 ) ( n - 3 ) ( n - 4 ) !

n and ( n - 4 ) ! gets cancelled on both sides. Hence we get,

=> 1 = 12 / ( n - 3 ) ( n - 2 )

=> ( n - 3 ) ( n - 2 ) = 12

=> n² - 3n - 2n + 6 = 12

=> n² - 5n + 6 - 12 = 0

=> n² - 5n - 6 = 0

=> n² - 6n + n - 6 = 0

=> n ( n - 6 ) + 1 ( n - 6 ) = 0

=> ( n + 1 ) ( n - 6 ) = 0

=> n = -1, 6

n cannot be negative, so n is 6

Hence the number of boys in the group is 6.

Answer 2

Hello!

Question
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In a group of boys, the number of arrangement of 4 boys is 12 times the number of arrangement of 2 boys. The number of boys in the group is

Solution:-
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Let the number of boys be x.

=> xP4 = 12*xP2

=> x!/(x-4)! = 12*x!/(x-2)!

=> (x-2)!/(x-4)! = 12

=> (x-2)(x-4) = 12

=> x^2-5x-6 = 0

=> (x-6)(x+1) = 0

=> x = 6

Therefore, The number of boys in the group is 6.

Hope It Helps!