Permutation question below

Question

A club has 30 members under the age of 30 and 40 members who are 30 or older. In how many ways can a slate of 6 officers be chosen if the President and atleast one other officer must be at least 30 years old?

Side note: the slate of officers is President, VP, Secretary, treasure, Press, and math consultant

 

Permutatuion question

Answer 1

The main restriction in this problem is that 2 of the officers have to be from the over 30 group.  Everyone else can come from any age group.  Remember the counting principal allows us to multiply the outcomes of each event so that the total can be calculated.

 

The first set is calculated by ₄₀P₂, while the second set is calculated by ₆₈P₄ (since two have already been picked.

 

Therefore: ₄₀P_{2 • 68}P₄ ≈ 3.05 x 10¹⁰ ways.