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 does not contain pant. (Enter the answer correct to two 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 does not contain pant. (Enter the answer correct to two decimal places)
Solution
To solve this problem, we first need to find the total number of ways to select 3 clothes from the 22 available (7 shirts, 5 pants, and 10 t-shirts). This can be calculated using the combination formula: C(n, r) = n! / [(r!(n-r)!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial.
Total number of ways to select 3 clothes from 22 = C(22, 3) = 22! / [(3!(22-3)!] = 1540 ways.
Next, we need to find the total number of ways to select 3 clothes without any pants. This means we can only choose from the 17 items that are not pants (7 shirts and 10 t-shirts).
Total number of ways to select 3 clothes from 17 (no pants) = C(17, 3) = 17! / [(3!(17-3)!] = 680 ways.
The probability that the randomly chosen clothes do not contain a pant is then the number of favorable outcomes (no pants) divided by the total number of outcomes.
Probability = 680 / 1540 = 0.44155844155844154.
Rounded to two decimal places, the probability is 0.44.
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