To solve this problem, we first need to understand the total number of ways Pramod can select 3 clothes from the given 24 clothes (5 shirts, 6 pants, and 13 t-shirts).

Step 1: Calculate total number of ways to select 3 clothes from 24.
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, total ways = C(24, 3) = 24! / [(24-3)! * 3!] = 2024 ways.

Step 2: Calculate the number of ways to select 3 clothes of different types.
This can be calculated as the product of the ways to select one item of each type.
So, favorable ways = C(5, 1) * C(6, 1) * C(13, 1) = 5! / [(5-1)! * 1!] * 6! / [(6-1)! * 1!] * 13! / [(13-1)! * 1!] = 5 * 6 * 13 = 390 ways.

Step 3: Calculate the probability.
The probability is the ratio of the favorable ways to the total ways.
So, Probability = favorable ways / total ways = 390 / 2024 = 0.1926 (approximately).

So, the probability that the randomly chosen clothes are of different types is approximately 0.1926 or 19.26%.

Question

To solve this problem, we first need to understand the total number of ways Pramod can select 3 clothes from the given 24 clothes (5 shirts, 6 pants, and 13 t-shirts).

Step 1: Calculate total number of ways to select 3 clothes from 24.
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, total ways = C(24, 3) = 24! / [(24-3)! * 3!] = 2024 ways.

Step 2: Calculate the number of ways to select 3 clothes of different types.
This can be calculated as the product of the ways to select one item of each type.
So, favorable ways = C(5, 1) * C(6, 1) * C(13, 1) = 5! / [(5-1)! * 1!] * 6! / [(6-1)! * 1!] * 13! / [(13-1)! * 1!] = 5 * 6 * 13 = 390 ways.

Step 3: Calculate the probability.
The probability is the ratio of the favorable ways to the total ways.
So, Probability = favorable ways / total ways = 390 / 2024 = 0.1926 (approximately).

So, the probability that the randomly chosen clothes are of different types is approximately 0.1926 or 19.26%.

Knowee AI · Accepted Answer

To solve this problem, we first need to understand the total number of ways Pramod can select 3 clothes from the given 24 clothes (5 shirts, 6 pants, and 13 t-shirts).

Step 1: Calculate total number of ways to select 3 clothes from 24.
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, total ways = C(24, 3) = 24! / [(24-3)! * 3!] = 2024 ways.

Step 2: Calculate the number of ways to select 3 clothes of different types.
This can be calculated as the product of the ways to select one item of each type.
So, favorable ways = C(5, 1) * C(6, 1) * C(13, 1) = 5! / [(5-1)! * 1!] * 6! / [(6-1)! * 1!] * 13! / [(13-1)! * 1!] = 5 * 6 * 13 = 390 ways.

Step 3: Calculate the probability.
The probability is the ratio of the favorable ways to the total ways.
So, Probability = favorable ways / total ways = 390 / 2024 = 0.1926 (approximately).

So, the probability that the randomly chosen clothes are of different types is approximately 0.1926 or 19.26%.

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, randomly chosen clothes are of different type.

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