Answer:
The number of ways is 6435
Step-by-step explanation:
Given
[tex]Male = 6[/tex]
[tex]Female = 5[/tex]
[tex]Students = 4[/tex]
Required
Number of ways a group of 8 can be formed
Here, I'll assume each category of people are distinct:
Hence;
[tex]Total = Male + Female + Students[/tex]
[tex]Total = 6 + 5 + 4[/tex]
[tex]Total = 15[/tex]
Number of ways is then calculated as follows:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
Where
[tex]n = 15\ and\ r = 8[/tex]
So, we have:
[tex]^{15}C_8 = \frac{15!}{(15 - 8)!8!}[/tex]
[tex]^{15}C_8 = \frac{15!}{7! * 8!}[/tex]
[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9 * 8!}{7!8!}[/tex]
[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7!}[/tex]
[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7 * 6 *5 * 4 * 3 * 2 * 1}[/tex]
[tex]^{15}C_8 = \frac{32432400}{5040}[/tex]
[tex]^{15}C_8 = 6435[/tex]
Hence, the number of ways is 6435
