Question

C(61,57)-C(60,56) evaluate this using C(n,r)+C(n,r-1)=C(n+1,r)​

Answer 1

To find :

⁶¹C₅₇ − ⁶⁰C₅₆

$∵ \: _{n}C _{r} + _{n}C _{(r - 1)} = _{(n + 1)}C _{r}$

$\implies _{n + 1}C _{r} - _{n}C _{r - 1} = _{n}C _{r}$

$\implies(_{61}C _{57} )- (_{60}C _{56} )=( _{60}C _{57})$

$\implies_{61}C _{57} - _{60}C _{56} = \frac{60!}{(57!)(60 - 57)!}$

$\implies_{61}C _{57} - _{60}C _{56} = \frac{60 \times 59 \times 58}{3 \times 2 \times 1}$

$\implies(_{61}C _{57} )- (_{60}C _{56} ) = 34220$