How many ways are there to choose 4 people out of 10 people to form a 7-member c

Question

How many ways are there to choose 4 people out of 10 people to form a 7-member committee? In how many different orders can 9 runners finish a race if no ties are allowed? In how many different orders can 9 runners finish a race if two people tie for the first place, three people tie for second place, and no ties otherwise? A coin is tossed 8 times. Each outcome will be a sequence of 8 heads and/or tails. What is the number of outcomes where the number of heads is exactly 3? Suppose that in a state, all car license plates consist of 3 capital letters followed by 4 digits. How many different license plates are possible? How many possible plates start with "ABC" and end with an even digit? How many plates are possible if all the letters and digits are distinct? A combination lock requires three selections of numbers, each from 1 through 20. How many different "combinations" are possible? How many "combinations" are possible if no number can be used twice? One earn contains 22 balls where: 5 balls are red (labeled R_i, R_.2,R_5), 7 are blue (labeled B_i,B_2,...;B_7), and 10 are white (labeled Wi; W2,W10). You draw 9 balls from the urn. What is the number of possible outcomes where 2 of the drawn balls are red, 3 are blue, and 4 are white?

Explanation / Answer

a) 10C4 210 b) 9! 362880 c) 9!/2!3! 30240 d) H=3 8C3 56 e) 26^3 (10^4) if repitition allowed 26C3(10C4) if repitition not allowed    ii) 1(10C3) 120 f) 20^3 8000 20C3 1140 g) 5C2(7C3)(10C4) 73500

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