Question

Suppose we want to choose to letters without replacement three letters a b and c. How many ways can this be done if the order of the choices is relevant? How many ways can this be done if the order of the choices is not relevant?

Answer 1

6 ;

3

Explanation:

Letters = (a, b, c)

Number of letters to be chosen = 2

If the order is relevant, then we use permutation :

nPr = n! ÷ (n-r)!

3P2 = 3! ÷ (3-2)!

3P2 = (3 * 2 * 1) ÷ 1

3P2 = 6

If the order is not relevant ; We use combination :

nCr = n! ÷ (n-r)!r!

3C2 = 3! ÷ (3-2)!2!

3C2 = 3! ÷ 1!2!

3C2 = (3 * 2!) ÷ 2! * 1

3C2 = 3