SOLUTION: In how many ways can a president, vice-president, and secretary be chosen from a class of 20 females and 30 males if the president must be a female and the vice president a male?

Algebra.Com
Question 1172162: In how many ways can a president, vice-president, and secretary be chosen from a class of 20 females and 30 males if the president must be a female and the vice president a male?
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Let's choose P, VP, then S... this is the most straightforward way to go:

(20C1)(30C1)(48C1) = 20*30*48 =
The 48 comes from the total 50 - 1 (female for P) - 1 (male for VP) = 48


But, you say, what if you choose S first?
Ok, let's do that case.

Choose S first, then P, then VP:
Two independent ways to choose S: (i) female, (ii) male

(i) female S: (20C1)(19C1)(30C1) = 20*19*30 = 11400

PLUS

(ii) male S: (30C1)(20C1)(29C1) = 30*20*29 = 17400


The total # of ways is 11400+17400 = 28800, just as we obtained before.




RELATED QUESTIONS

In how many ways can a president, vice president and secretary be chosen from a class of... (answered by stanbon)
In how many ways can a president, vice president, and secretary be chosen from a class of (answered by ikleyn)
In how many different ways can a president, vice president and secretary be elected from... (answered by jorel1380)
in how many ways can people chosen from a group of 8 be voted President, Vice President,... (answered by Alan3354)
In how many ways can a president, vice president, and secretary be randomly selected from (answered by ewatrrr)
How many ways can a school organization officers consisting of a president, a... (answered by Edwin McCravy)
How many ways can a president, vice-president, and secretary be chosen from a... (answered by checkley79)
how many ways can a president, vice-president, treasurer, and secretary be chosen from a... (answered by ikleyn)
A committee consists of a President, a Vice President, a Treasurer, and a Secretary. The (answered by jorel1380)