Question

I need help with 2 math questions evaluating subscripts

Evaluate _[8]C_[4] and _[7]P_[4]

Answer 1

1.

`^8C_4=(2 * 7 * 5)/(1 ) = 70`

2.

`^7P_4 = 210`

Explanation:

1. We want to evaluate

`^8C_4`

Recall that:

`^nC_r= (n!)/((n - r)!r ! )`

`^8C_4= (8!)/((8- 4)!4! )`

`^8C_4=(8!)/(4!4! )`

`^8C_4=(8 * 7 * 6 * 5 * 4!)/(4!4! )`

`^8C_4=(8 * 7 * 6 * 5 * 4!)/(4* 3 * 2 * 1 * 4! )`

`^8C_4=(8 * 7 * 6 * 5 )/(4* 3 * 2 * 1)`

`^8C_4=(2 * 7 * 5)/(1 ) = 70`

2. We want to evaluate

`^7P_4`

`^nP_r = (n!)/((n - r)!)`

`^7P_4 = (7!)/((7 - 4)!)`

`^7P_4 = (7!)/(3!)`

`^7P_4 = (7 * 6 * 5 * 4* 3!)/(3!)`

`^7P_4 = (7 * 6 * 5* 4 )/(1) = 840`