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How many ways can you pick a president, a vice president, a secretary and a treasurer out of 28 people for student council?

How many ways can you pick a president, a vice president, a secretary and a treasurer out of $28$ people for student council?

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Compound events: find the number of outcomes

Full solution

Q. How many ways can you pick a president, a vice president, a secretary and a treasurer out of

28

people for student council?

Understand the problem: Understand the problem. $\newline$ We need to find the number of different ways to choose $4$ different positions from a group of $28$ people. This is a permutation problem because the order in which we select the people for the different positions matters.
Calculate president: Calculate the number of ways to choose the president. $\newline$ There are $28$ people to choose from for the president position. So, there are $28$ possible choices for president.
Calculate vice president: Calculate the number of ways to choose the vice president. $\newline$ After choosing a president, we have $27$ people left to choose from for the vice president position. So, there are $27$ possible choices for vice president.
Calculate secretary: Calculate the number of ways to choose the secretary. $\newline$ After choosing a president and a vice president, we have $26$ people left to choose from for the secretary position. So, there are $26$ possible choices for secretary.
Calculate treasurer: Calculate the number of ways to choose the treasurer. $\newline$ After choosing a president, a vice president, and a secretary, we have $25$ people left to choose from for the treasurer position. So, there are $25$ possible choices for treasurer.
Calculate total: Calculate the total number of ways to choose all four positions. $\newline$ To find the total number of ways to choose all four positions, we multiply the number of choices for each position together. $\newline$ Total number of ways $= 28$ (president) $\times 27$ (vice president) $\times 26$ (secretary) $\times 25$ (treasurer)
Perform calculation: Perform the calculation. $\newline$ Total number of ways $= 28 \times 27 \times 26 \times 25$ $\newline$ $= 1,891,800$

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