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The number of ways of choosing a committee of 4 women and 5 men from 10 women and 9 men, If Mr. A refuse to serve on committee, if Mr. B is a member of the committee, can not exeed.
  • a)
    26460
  • b)
    28460
  • c)
    29230
  • d)
    none
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The number of ways of choosing a committee of 4 women and 5 men from 1...
 Total women = 10
total men = 9
choosing committee = 4 w and 3 m

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Most Upvoted Answer
The number of ways of choosing a committee of 4 women and 5 men from 1...
To solve this problem, we need to consider the following conditions:

1. We need to choose a committee of 4 women and 5 men.
2. Mr. A refuses to serve on the committee.
3. Mr. B is a member of the committee.
4. The total number of committee members cannot exceed a certain value.

Let's break down the solution step by step:

Step 1: Finding the number of ways to select 4 women from 10 women
We can use the combination formula to find the number of ways to choose 4 women from a group of 10 women:
C(10, 4) = 10! / (4! * (10-4)!) = 210

Step 2: Finding the number of ways to select 5 men from 9 men
Using the same combination formula, we can find the number of ways to choose 5 men from a group of 9 men:
C(9, 5) = 9! / (5! * (9-5)!) = 126

Step 3: Considering the condition that Mr. A refuses to serve on the committee
Since Mr. A refuses to serve on the committee, we need to subtract 1 from the total number of men we can choose from. Therefore, the number of ways to select 5 men from 8 men becomes:
C(8, 5) = 8! / (5! * (8-5)!) = 56

Step 4: Considering the condition that Mr. B is a member of the committee
Since Mr. B is a member of the committee, we have already selected 1 man. Therefore, we only need to select 4 more men from the remaining group of men, which is 7. So the number of ways to select 4 more men from 7 men becomes:
C(7, 4) = 7! / (4! * (7-4)!) = 35

Step 5: Calculating the total number of ways to form the committee
To calculate the total number of ways to form the committee, we multiply the number of ways to choose women and men together:
Total number of ways = 210 * 56 * 35 = 411,600

Step 6: Checking the given condition
The problem states that the total number of ways cannot exceed a certain value. From the given options, the maximum value is 29,230. Since the calculated number of ways (411,600) exceeds this maximum value, the correct answer is option D, none.

In conclusion, the correct answer is option D, none.
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The number of ways of choosing a committee of 4 women and 5 men from 10 women and 9 men, If Mr. A refuse to serve on committee, if Mr. B is a member of the committee, can not exeed.a)26460b)28460c)29230d)noneCorrect answer is option 'D'. Can you explain this answer?
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