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  • A teacher has a class of 20 students and wants to divide them into groups of 4 for a project. Each group must have a designated leader. How many different ways are there to choose the le

A teacher has a class of 20 students and wants to divide them into groups of 4 for a project. Each group must have a designated leader. How many different ways are there to choose the leaders for each group, if the same student can be a leader for more than one group?

Option: 1

120000


Option: 2

140000


Option: 3

160000


Option: 4

150000


Answers (1)

best_answer

Given that,

20 students are in a class, and the teacher wants to break them into groups of four for a project.

Since the same student can be a leader for more than one group, there are no restrictions on who can be chosen as the leader for each group. 

Therefore, for each group, we have 20 choices for the leader. Since there are 4 groups, the total number of ways to choose the leaders for each group is given by,

\begin{aligned} &20^4=20 \times 20 \times 20 \times 20\\ &20^4=160000 \end{aligned}

Therefore, there are 160000 different ways to choose the leaders for each group if the same student can be a leader for more than one group.

 

Posted by

Ritika Jonwal

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