The given expression is [tex] ^7P_6-2(^6C_2) [/tex]
Here P represents Permutation and C represents Combination
Thus, the given expression can be rewritten as:
[tex] ^7P_6-2(^6C_2)=\frac{7!}{(7-6)!}-2\frac{6!}{(6-2)!2!} =\frac{7!}{1!}-2\frac{6!}{4!2!} [/tex]
[tex] \therefore ^7P_6-2(^6C_2)=7!-\frac{2\times 6\times 5\times 4!}{4!\times 2}=5040-30=5010 [/tex]
Therefore, for the given expression [tex] ^7P_6-2(^6C_2) [/tex], it's value is 5010
