Pramod goes to a shop to buy some clothes. Shopkeeper shows him 5 shirts, 6 pants and 13 t-shirts. If he selects three clothes at random, then find the probability that, at least one of the clothes is shirt.
Question
Pramod goes to a shop to buy some clothes. Shopkeeper shows him 5 shirts, 6 pants and 13 t-shirts. If he selects three clothes at random, then find the probability that, at least one of the clothes is shirt.
Solution
Step 1: First, we need to calculate the total number of ways Pramod can select 3 clothes from the given 24 clothes (5 shirts, 6 pants, and 13 t-shirts). This can be done using the combination formula, which is nCr = n! / r!(n-r)!. Here, 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 from 24 is 24C3.
Step 2: Next, we calculate the number of ways to select 3 clothes without a shirt. This means we are only choosing from the 6 pants and 13 t-shirts, which is a total of 19 clothes. So, the number of ways to select 3 clothes from 19 (without a shirt) is 19C3.
Step 3: The probability that at least one of the clothes is a shirt is 1 minus the probability that none of the clothes is a shirt. So, we subtract the number of ways to select 3 clothes without a shirt from the total number of ways to select 3 clothes, and then divide by the total number of ways to select 3 clothes.
So, the probability that at least one of the clothes is a shirt is (24C3 - 19C3) / 24C3.
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