If-n-C-3-n-C-2-14-Find-n-P-2-

Question Number 150289 by mathdanisur last updated on 10/Aug/21

If_{n} C_{3} -_{n} C_{2} = 14

Find_{n} P_{2} = ?

Answered by Ar Brandon last updated on 12/Aug/21

\overset{n}{} C_{3} - \overset{n}{} C_{2} = 14

\frac{n!}{(n - 3)! 3!} - \frac{n!}{(n - 2)! 2!} = 14

\frac{n! (n - 2 - 3)}{(n - 2)! 3!} = \frac{n (n - 1) (n - 5)}{3!} = 14

n^{3} - 6 n^{2} + 5 n - 84 = 0, n = 7

\overset{7}{} P_{2} = \frac{7!}{5!} = 42

Commented by mathdanisur last updated on 10/Aug/21

S er, Thank You

Commented by mathdanisur last updated on 11/Aug/21

S er, n = 5 or n = 7 . ?

Commented by Ar Brandon last updated on 12/Aug/21

Thanks . Edited!