Question

I need help with 2 math questions evaluating subscripts

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

Answer 1

Answer:

1.

$^8C_4=\frac{2 \times 7 \times 5}{1 } = 70$

2.

$^7P_4 = 210$

Step-by-step explanation:

1. We want to evaluate

$^8C_4$

Recall that:

$^nC_r= \frac{n!}{(n - r)!r ! }$

$^8C_4= \frac{8!}{(8- 4)!4! }$

$^8C_4=\frac{8!}{4!4! }$

$^8C_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4!4! }$

$^8C_4=\frac{8 \times 7 \times 6 \times 5 \times 4!}{4\times 3 \times 2 \times 1 \times 4! }$

$^8C_4=\frac{8 \times 7 \times 6 \times 5 }{4\times 3 \times 2 \times 1}$

$^8C_4=\frac{2 \times 7 \times 5}{1 } = 70$

2. We want to evaluate

$^7P_4$

$^nP_r = \frac{n!}{(n - r)!}$

$^7P_4 = \frac{7!}{(7 - 4)!}$

$^7P_4 = \frac{7!}{3!}$

$^7P_4 = \frac{7 \times 6 \times 5 \times 4\times 3!}{3!}$

$^7P_4 = \frac{7 \times 6 \times 5\times 4 }{1} = 840$