Question

Simplify `(C_2^7xxC_3^6)/(C_3^7xxC_4^5)`?

Answer 1

`(C_2^7xxC_3^6)/(C_3^7xxC_4^5)=12/5`

Explanation:

`C_r^n=(n!)/(r!(n-r)!)=(n(n-1)(n-2)...(n-r+1))/(1*2*....*r)`

Hence `(C_2^7xxC_3^6)/(C_3^7xxC_4^5)`

= `((7xx6)/(1xx2)xx(6xx5xx4)/(1xx2xx3))/((7xx6xx5)/(1xx2xx3)xx(5xx4xx3xx2)/(1xx2xx3xx4))`

= `(21xx20)/(35xx5)`

= `(cancel21^3xxcancel20^4)/(cancel35^5xxcancel5^1)`

= `12/5`