Question

Find the value of n, if P(n,2)=3.c(n,3).

Answer 1

SOLUTION

GIVEN

P(n,2) = 3.C(n,3)

TO DETERMINE

The value of n

EVALUATION

Here it is given that

P(n,2) = 3.C(n,3)

$\displaystyle \sf{ \implies {}^{n} P_2 = 3. {}^{n} C_3}$

$\displaystyle \sf{ \implies \frac{n!}{(n - 2)!} = 3 \times \frac{n!}{(n - 3)!3!} }$

$\displaystyle \sf{ \implies \frac{1}{(n - 2)!} = 3 \times \frac{1}{(n - 3)!3!} }$

$\displaystyle \sf{ \implies \frac{(n - 3)!}{(n - 2)!} = \frac{3}{3!} }$

$\displaystyle \sf{ \implies \frac{(n - 2)!}{(n - 3)!} = \frac{3!}{3} }$

$\displaystyle \sf{ \implies \frac{(n - 2) \times (n - 3)!}{(n - 3)!} = \frac{3 \times 2}{3} }$

$\displaystyle \sf{ \implies (n - 2) = 2 }$

$\displaystyle \sf{ \implies n = 4 }$

FINAL ANSWER

Hence the required value of n = 4

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