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From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is?
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From a group of 5 men and 7 women, five persons are to be selected to ...
Problem Statement: From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. Find the number of ways this can be done.
Solution:
To solve this problem, we will use the combination formula.
Step 1: Find the total number of ways to select 5 people from a group of 12.
Total number of ways = 12C5 = (12!/5!7!) = 792
Step 2: Find the number of ways to select a committee with no men.
Number of ways to select 5 women from 7 = 7C5 = (7!/5!2!) = 21
Step 3: Find the number of ways to select a committee with only 1 or 2 men.
Number of ways to select 1 man and 4 women = 5C1 * 7C4 = 5 * 35 = 175
Number of ways to select 2 men and 3 women = 5C2 * 7C3 = 10 * 35 = 350
Total number of ways to select a committee with 1 or 2 men = 175 + 350 = 525
Step 4: Find the number of ways to select a committee with at least 3 men.
Number of ways to select a committee with 3 men and 2 women = Total number of ways - Number of ways to select a committee with no men - Number of ways to select a committee with only 1 or 2 men
= 792 - 21 - 525 = 246
Therefore, the number of ways to select a committee with at least 3 men is 246.
Solution:
To solve this problem, we will use the combination formula.
Step 1: Find the total number of ways to select 5 people from a group of 12.
Total number of ways = 12C5 = (12!/5!7!) = 792
Step 2: Find the number of ways to select a committee with no men.
Number of ways to select 5 women from 7 = 7C5 = (7!/5!2!) = 21
Step 3: Find the number of ways to select a committee with only 1 or 2 men.
Number of ways to select 1 man and 4 women = 5C1 * 7C4 = 5 * 35 = 175
Number of ways to select 2 men and 3 women = 5C2 * 7C3 = 10 * 35 = 350
Total number of ways to select a committee with 1 or 2 men = 175 + 350 = 525
Step 4: Find the number of ways to select a committee with at least 3 men.
Number of ways to select a committee with 3 men and 2 women = Total number of ways - Number of ways to select a committee with no men - Number of ways to select a committee with only 1 or 2 men
= 792 - 21 - 525 = 246
Therefore, the number of ways to select a committee with at least 3 men is 246.
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From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is?
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From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is?.
From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee.the number of ways this can done is?.
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