Pramod goes to a shop to buy some clothes. Shopkeeper shows him 7 shirts, 5 pants and 10 t-shirts. If he selects three clothes at random, then find the probability that, randomly chosen clothes are of different type. (Enter the answer correct to three decimal places)
Question
Pramod goes to a shop to buy some clothes. Shopkeeper shows him 7 shirts, 5 pants and 10 t-shirts. If he selects three clothes at random, then find the probability that, randomly chosen clothes are of different type. (Enter the answer correct to three decimal places)
Solution
To solve this problem, we first need to calculate the total number of ways to select 3 clothes out of 22 (7 shirts + 5 pants + 10 t-shirts).
This can be calculated using the combination formula: C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose.
So, the total number of ways to select 3 clothes out of 22 is C(22, 3) = 22! / [(22-3)! * 3!] = 1540.
Next, we need to calculate the number of ways to select 3 clothes such that each is of a different type. This can be done by selecting 1 shirt, 1 pant, and 1 t-shirt.
The number of ways to do this is C(7, 1) * C(5, 1) * C(10, 1) = 7 * 5 * 10 = 350.
Finally, the probability that the 3 randomly chosen clothes are of different types is the number of favorable outcomes divided by the total number of outcomes.
So, the probability is 350 / 1540 = 0.227.
Therefore, the probability that the 3 randomly chosen clothes are of different types is approximately 0.227 or 22.7% when rounded to three decimal places.
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