How many different arrangements ?

Question

If a club consist of 10 members, how many different arrangements of president, vice-president, and secretary are possible?

Answer 1

As long as each office can be held by only 1 person and and nobody can hold more than one office, than solve the problem using permutations.

 

₁₀P_{3 = 10!/(10-3)! = 3628800/5040 = 720 Therefore there are 720 possible different arrangements.}

 

Remember that 10! is read 10 factorial and means that you multiply 10x9x8x7x6x5x4x3x2x1.

(10-3)! would indicate subtracting 10 - 3 first because of order of operations. Your answer is 7! or 7 factorial. This means you multiply 7x6x5x4x3x2x1. Then you divide the products to get the final answer of 720.

 

Finally, ₁₀P_{3 means you have a permutation of  a total 10 things or in this case people. Using all 10, it tells how many different ways can you arrange 3 of them.  That's where the formula comes from: 10! (the number before P) divided by (10-3)! (the number before P minus the number after P).}

 

I hope this was helpful.

Answer 2

10 x 9 x 8 = 720