Answer:
B. 1 out of 5,005
Step-by-step explanation:
Given
Number of Friends = 15
Required
Probability of selecting 6 friends
The first step is to calculate the number of ways 6 friends can be selected
The keyword in the above statement is selection;
This implies combination;
The number of ways is calculated as follows;
[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]
Where n = 15 and r = 6
[tex]\left[\begin{array}{c}n&r&\end{array}\right] = \frac{n!}{(n-r)!r!}[/tex]
becomes
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{(15-6)!6!}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15!}{9!6!}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10 * 9!}{9! *6 * 5 * 4 * 3 * 2 * 1}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{15 * 14 * 13 * 12 * 11 *10}{6 * 5 * 4 * 3 * 2 * 1}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] = \frac{3603600}{720}[/tex]
[tex]\left[\begin{array}{c}15&6&\end{array}\right] =5005[/tex]
Hence, there are 5005 ways of selecting 6 from 15 friends
Since, there's only one way of selecting the 6 named friends
Then, the probability is 1 out of 5,005
