There are 20 athletes and 30 non athletes. A group of 10 must be made. How many if non restricted? How many if half from each? How much if 7 athletes and 3 non athletes? Use combos and permutations and Pascal’s triangle

Relevance
• Non restricted = 50C10 = 50!/[(40!)(10!)] = 10,272,278,170.

If half from each = 20C5 * 30C5 = (20!)(30!)/[(25!)(15!)(5!)^2] = 2,209,413,024.

if 7 athletes and 3 non athletes = 20C7 * 30C3 = (20!)(30!)/[13!)(7!)(27!)(3!) = 314,731,200.

• Log in to reply to the answers
• Q1: How many if non restricted?

A: From all 50 choose 10

C(50,10)

Q2: How many if half from each?

A: From 20 choose 5 and from 30 choose 5

C(20,5) * C(30,5)

Q3: How many if 7 athletes and 3 non athletes?

A: From 20 choose 7 and from 30 choose 3

C(20,7) * C(30,3)

P.S. You can double check your answers with Google. For example, type "20 choose 7 * 30 choose 3"

• Log in to reply to the answers
• If unrestricted, 50c10

If half and half, 30c5 * 20c5

If seven athletes, 20c7 * 30c3

• Log in to reply to the answers