Question

Evaluate 7P6 − 2(6C2)

Answer 1

Multiply 6 by -2 to get -12

7x6-12y2

Answer 2

The given expression is $^7P_6-2(^6C_2)$

Here P represents Permutation and C represents Combination

Thus, the given expression can be rewritten as:

$^7P_6-2(^6C_2)=\frac{7!}{(7-6)!}-2\frac{6!}{(6-2)!2!} =\frac{7!}{1!}-2\frac{6!}{4!2!}$

$\therefore ^7P_6-2(^6C_2)=7!-\frac{2\times 6\times 5\times 4!}{4!\times 2}=5040-30=5010$

Therefore, for the given expression $^7P_6-2(^6C_2)$, it's value is 5010