Question

3. The dance club at school has 22 members. The dance coach wants to send four members to a special training on

new dance routines.
a. The dance coach will select four dancers to go to the special training. Is the number of ways to select four
dancers a permutation, a combination, or neither? Explain your answer.
b. If the dance coach chooses at random, how would you determine the probability of selecting dancers Laura,
Matthew, Lakiesha, and Santos?

Answer 1

a) a combination

b) The probability = 1 ÷ [ Number of ways to select the four dancers ]

Explanation:

a) Here it is only required to calculate the number of ways to select the four dancers and the order of the dancers is not required i.e not important for us.

Hence, we will use a combination to select 4 out of 22 dancers

i.e ²²C₄

b) Since the dancers selected are 4 predetermined individuals

therefore,

number of ways to select selecting dancers Laura, Matthew, Lakiesha, and Santos will be '1'

Hence,

The probability = 1 ÷ [ Number of ways to select the four dancers ]

= 1 ÷ ²²C₄