Question

1. In how many ways can a committee of eight people to be formed from a group of 6 male, 5 female and 4 students if there are no restrictions, as all members are eligible?

Answer 1

Answer:

The number of ways is 6435

Step-by-step explanation:

Given

$Male = 6$

$Female = 5$

$Students = 4$

Required

Number of ways a group of 8 can be formed

Here, I'll assume each category of people are distinct:

Hence;

$Total = Male + Female + Students$

$Total = 6 + 5 + 4$

$Total = 15$

Number of ways is then calculated as follows:

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

Where

$n = 15\ and\ r = 8$

So, we have:

$^{15}C_8 = \frac{15!}{(15 - 8)!8!}$

$^{15}C_8 = \frac{15!}{7! * 8!}$

$^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9 * 8!}{7!8!}$

$^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7!}$

$^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7 * 6 *5 * 4 * 3 * 2 * 1}$

$^{15}C_8 = \frac{32432400}{5040}$

$^{15}C_8 = 6435$

Hence, the number of ways is 6435