Question

there are 19 members in a committee. in how many different ways can a president vice president secretary and treasure be chosen

Answer 1

Given:

Total members in the committee = 19

Let's find the number of ways a president, vice president, secretary and treasurer can be chosen.

Here, we are to use permutation formula:

`^nP_r=(n!)/((n-r)!)`

Where:

n = 19

r = 4

Thus, we have:

`\begin{gathered} ^(19)P_4=(19!)/((19-4)!) \\ \\ ^(19)P_4=(19!)/((15)!) \\ \\ =(19*18*17*16*15!)/(15!) \\ \\ =19*18*17*16 \\ \\ =93024 \end{gathered}`

Solving further:

Therefore, the number of ways they can be chosen is 93024 ways.

ANSWER:

93024 ways