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A bag contains 3 "W"s, 3 "I"s, and 3 "N"s. Pull 3 tiles out of the bag. Do not put them back once you take them out.

a) How many possible combinations of tiles can be drawn?
b) Calculate the probability of drawing three "I"s.

User TheBen
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1 Answer

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Final answer:

The number of possible combinations of 3 tiles that can be drawn from the bag is 84, and the probability of drawing three "I"s without replacement is 1/84.

Step-by-step explanation:

The question asks to determine the number of possible combinations of tiles that can be drawn from a bag containing 3 "W"s, 3 "I"s, and 3 "N"s, as well as to calculate the probability of drawing three "I"s without replacement.

a) Number of Possible Combinations:

To find the number of possible combinations of 3 tiles that can be drawn from the bag, we can use the combination formula C(n, k) = n! / (k! * (n-k)!), where n is the total number of tiles and k is the number of tiles drawn. Here, n = 9 (since there are 3 Ws, 3 Is, and 3 Ns) and k = 3. Thus, the number of possible combinations is C(9, 3) = 9! / (3! * (9-3)!) = 84 combinations.

b) Probability of Drawing Three "I"s:

To calculate the probability of drawing three "I"s without replacement, we use the multiplicative rule of probability. The probability for the first "I" is 3/9, for the second is 2/8 after one "I" is removed, and for the third is 1/7 after two "I"s are removed. Hence, the probability is (3/9) * (2/8) * (1/7) = 1/84.

User Daniel Casserly
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