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A company employed 7CA's ,6 MBA's and 3 Engineer's .In how many ways the company can form a commitee ,if the committee has two members of each type.?
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A company employed 7CA's ,6 MBA's and 3 Engineer's .In how many ways t...
**Solution:**

To form a committee with two members of each type (7CA's, 6 MBA's, and 3 Engineers), we need to select 2 members from each category.

We can solve this problem using the concept of combinations.

Let's solve this step by step:

**Selecting 2 CA's from 7CA's:**

We need to select 2 CA's from a group of 7CA's.
This can be done using the combination formula: nCr = n! / ((n-r)! * r!)

n = 7 (number of CA's)
r = 2 (number of members to be selected)

7C2 = 7! / ((7-2)! * 2!) = 7! / (5! * 2!) = (7*6*5!) / (5!*2*1) = (7*6) / (2*1) = 21

Therefore, there are 21 ways to select 2 CA's from 7CA's.

**Selecting 2 MBA's from 6 MBA's:**

We need to select 2 MBA's from a group of 6 MBA's.
Using the same combination formula:

n = 6 (number of MBA's)
r = 2 (number of members to be selected)

6C2 = 6! / ((6-2)! * 2!) = 6! / (4! * 2!) = (6*5*4!) / (4!*2*1) = (6*5) / (2*1) = 15

Therefore, there are 15 ways to select 2 MBA's from 6 MBA's.

**Selecting 2 Engineers from 3 Engineers:**

We need to select 2 Engineers from a group of 3 Engineers.
Using the same combination formula:

n = 3 (number of Engineers)
r = 2 (number of members to be selected)

3C2 = 3! / ((3-2)! * 2!) = 3! / (1! * 2!) = (3*2*1!) / (1!*2*1) = (3*2) / (2*1) = 3

Therefore, there are 3 ways to select 2 Engineers from 3 Engineers.

**Combining the Results:**

Now, we need to find the total number of ways to form the committee by selecting members from each category simultaneously.

To find the total number of ways, we need to multiply the number of ways of selecting members from each category.

Total number of ways = Number of ways to select 2 CA's * Number of ways to select 2 MBA's * Number of ways to select 2 Engineers

= 21 * 15 * 3

= 945

Therefore, the company can form the committee in 945 different ways.
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A company employed 7CA's ,6 MBA's and 3 Engineer's .In how many ways the company can form a commitee ,if the committee has two members of each type.?
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A company employed 7CA's ,6 MBA's and 3 Engineer's .In how many ways the company can form a commitee ,if the committee has two members of each type.? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A company employed 7CA's ,6 MBA's and 3 Engineer's .In how many ways the company can form a commitee ,if the committee has two members of each type.? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A company employed 7CA's ,6 MBA's and 3 Engineer's .In how many ways the company can form a commitee ,if the committee has two members of each type.?.
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