Question

For her birthday, Monica can invite 6 of her 15 student friends to join her at a theme park. If she chooses to invite friends at random, what is the probability that friends Tessa,

Guido, Brendan, Faith, Charlotte and Rhianna are chosen?
10 out of 27,358
1 out of 5,005
1 out of 720
1 out of 3,603,600

Answer 1

B. 1 out of 5,005

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;

`\left[\begin{array}{c}n&r&\end{array}\right] = (n!)/((n-r)!r!)`

Where n = 15 and r = 6

`\left[\begin{array}{c}n&r&\end{array}\right] = (n!)/((n-r)!r!)`

becomes

`\left[\begin{array}{c}15&6&\end{array}\right] = (15!)/((15-6)!6!)`

`\left[\begin{array}{c}15&6&\end{array}\right] = (15!)/(9!6!)`

`\left[\begin{array}{c}15&6&\end{array}\right] = (15 * 14 * 13 * 12 * 11 *10 * 9!)/(9! *6 * 5 * 4 * 3 * 2 * 1)`

`\left[\begin{array}{c}15&6&\end{array}\right] = (15 * 14 * 13 * 12 * 11 *10)/(6 * 5 * 4 * 3 * 2 * 1)`

`\left[\begin{array}{c}15&6&\end{array}\right] = (3603600)/(720)`

`\left[\begin{array}{c}15&6&\end{array}\right] =5005`

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