Since we have to choose four persons from a group of five people, the first position for president can be covered in 5C1=5 ways, from the remaining four people we can choose vice president in 4C1=4 ways and the rest people will be elected in 3C2=3 ways.
So the committee can be formed in 5*4*3=60 ways.

We will choose people for each position in turn.

President:5 -> Vice President:4 -> Treasurers:3C2

-> Total = 5*4*3=60.

Since president and vice president are two unique positions, order matters when we select people for these positions. So 5 choices for the president post when a president has been selected we have 4 people for vice president post. which gives us 5*4 permutations are president and vice presidents. Now 3 people remain. of these 3 two will be selected for the treasury post. Since two people will have the same designation of treasury order does not matter. So we can select 2 treasuries our of three in 3 ways 3*2/2. Now the total combinations of presidents, vice presidents and treasuries =5*4*3=60

In this case ORDER MATTERS (Being picked as president is not equal to be picked as vice president, and so on), hence we have to use the permutation of 4 people out of 5.

5P4.

However, the two treasurers have equal importance as being selected as the first treasurer do not give you more importance than being the second treasurer.
Thus we remove this repetition:

5P4/2C1 = 5*4*3 = 60

Suddenly this becomes a verbal reasoning question.

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