Permutations and Combinations Classwork



Permutations and Combinations Classwork Name:_____________________________

Part I: Math with Factorials—Expand each factorial and solve each problem. Show all work. This is NOT to be done exclusively in your calculator.

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Part II: Find number of possibilities using the permutation and combination formulas. Show work by plugging numbers into the formulas before typing factorials into calculator. The formulas are given below!

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Part III: For each problem below, decide whether each problem is a Permutation or a Combination. Once you’ve decided, use the formula to find the number of possibilities.

13) The board of directors at the XYZ corporation has 15 members. In how many ways can they choose

a) A committee of 4 members (president, vp, treasurer, and secretary)?

b) A delegation of 4 members where all members have equal standing?

14) There are 10 horses entered in a race. In how many ways can one pick

a) the top three finishers regardless of order?

b) The first, second, and third place finishers in the race?

15) There are 20 singers auditioning for a musical. In how many different ways can the director choose

a) a duet?

b)A lead singer and a backup?

c) a quintet?

16) there are 117 Division I-A college football teams

a) How many Top 25 rankings are possible?

b) How many ways are there to choose 8 teams for a playoff?

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