Question

In a certain club there are 6 freshmen, 7 sophomores, 6 juniors, and 10th seniors. The club wishes to form a five member committee to investigate the problem of flying squirrel attacks. The committee is to be formed by selecting one member from each of the four classes, and then one at-large member. In how many ways can the committee be chosen?

Answer 1

the simplest way to obtain the correct answer is to divide by 2, since the overcounting will exactly double the answer, so

# of ways = 8*6*8*9*27/2 = 46,656 <---------

the longer way is 8c2*6*8*9 + 6c2*8*8*9 + 8c2*8*6*9 + 9c2*8*6*8Explanation: