I took a different tack. There are 6 interview slots. There are 18 men to choose from for the first slot, 15 for the second and 12 for the third. The choices decline by 3 because once a man is chosen for the interview, his two male team mates are excluded from the pool of male interviewees. The same sequence applies to the three women, i.e., 18,15 and 12. The product of 18*15*12*18*15*12 gives the number of ways you could choose the interviewees if the order in which they were interviewed mattered. It doesn't so you divide the product by 6! which is the number of ways to arrange 6 distinct interviewees. That works out to 14580.
In how many ways can the first six players of a volleyball team be chosen from a 15-member volleyball team Using the Combination Formula #CarryOnLearning . - Introduction to Combinations - PROOF of the formula on the number of Combinations - Problems on Combinations - OVERVIEW of lessons on Permutations and Combinations in this site. Also, you have this free of charge online textbook in ALGEBRA-II in this site - ALGEBRA-II - YOUR ONLINE TEXTBOOK. The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations". |