A group of 7 males..

Question

A group of 7 males and 7 females volunteer for a medical study. Three volunteers are selected.

How many ways can the three subjects be selected from the 14 volunteers?

How many selections contain at least two females?

How many selections contain at most one female?

Answer 1

choose 3 from 14

14!/(3!*11!)

(14*13*12)/(3*2)

14*13*2=364 ways

 

at least 2 females means 2 females or 3 females

find how many ways for 2 females plus how many ways for 3 females

2 females and 1 male plus 3 females and no males

7!/2!*5! times 7!/1!6! plus 7!/3!4!

7*6/2=21 times 7 plus 7*6*5/3*2=7*5

21*7+35=147+35=182

 

at most 1 female means 0 females or 1 female

find how many ways for 0 females plus how many ways for 1 female

0 females means 3 males

3 males plus 1 female times 2 males

7!/3!4! plus 7!/1!6! times 7!/2!*5!

7*6*5/3*2 plus 7 times 7*6/2

35+7*21=35+147=182