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.