The staff of a restaurant consists of 28 people (9 waiters, 13 waitresses and 6 cooks.) For Mother's Day, a total of 10 people will be selected to work. If the selections are made at random, determine the probability that 3 waiters 5 waitresses and 2 cooks will be selected.

Answer: 0.1236

Step-by-step explanation:

Probability that an outcome is recorded is the division of the total possibility of the outcome desired divided by the total possible outcomes that can be gotten.

probability = favourable outcome/possible outcome

In this case, the favourable outcome is having 3 waiters, 5 waitresses and 2 cooks from a possible 9 waiters, 13 waitresses and 6 cooks and the possible outcome is having the 10 people chosen randomly from the available 28without conditions.

To find the number of ways to choose this option, the combination formular for selection is used.

Number of ways for preferred outcome of 3 waiters, 5 waitresses and 2 cooks from available 9waiters, 13 waitresses and 6cooks become:

= 9C3 * 13C5 * 6C2 = 1621620 ways.

If there are no restrictions and this 10 people are chosen at random from the 28 available staff, then the number of ways is 28C10 = 13123110

Probability of having 3 waiters, 5 waitresses and 2 cooks from available options = 1621620/13123110 = 0.1236