The Greek alphabet has 24 letters. In how many ways can 5 different Greek letters be selected if the order does not matter?

Question

The Greek alphabet has 24 letters. In how many ways can 5 different Greek letters be selected if the order 

Answer 1

Jessica, to solve this question, use the formula for combinations: n!/(r!(n-r)!), where n is equal to 24 (the number of letters in the set), and r is equal to 5 (the subset). These can be plugged into a combinations calculator yielding an answer of 42,504.

 

If you had to work the problem longhand, set it up as follows: 24!/(5!(24-5)!). Now, expand the numerator so that the value is 24 x 23 x 22 x 21 x 20 x 19!- note this is key. The denominator is 5!(24-5)!), which expands to 5!(19)!. The 19! in the numerator and denominator cancel each other out, they equal 1, so you are left with a numerator value of 24 x 23 x 22 x 21 x 20 = 5100480, and a denominator of 5!, which equals 5 x 4 x 3 x 2 x 1 = 120. Division of 5100480 by 120 equals 42504.