Solveeit Logo
Login

Question

Mathematics Question on permutations and combinations

If m+nP2=90^{m+n}P{{ }_{2}}=90 and m−nP2=30,^{m-n}P{{ }_{2}}=30, then (m,n)(m,n) is given by (where, m and n are positive integers)

A

(8, 2)(8,\,2)

B

(5,  6)(5,\,\,6)

C

(3,  7)(3,\,\,7)

D

(8,  3)(8,\,\,3)

Answer

(8, 2)(8,\,2)

Explanation

Solution

By taking option [a], (m, n)=(8, 2)(m,\,n)=(8,\,2)
Now, m+nP2=8+2P2=10P2^{m+n}{{P}_{2}}{{=}^{8+2}}{{P}_{2}}{{=}^{10}}{{P}_{2}}
=10 !8!=90=\frac{10\,!}{8!}=90
and m−nP2=8−2P2=6P2^{m-n}{{P}_{2}}{{=}^{8-2}}{{P}_{2}}{{=}^{6}}{{P}_{2}}
=6!4!=30=\frac{6!}{4!}=30