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From his 9 friends (4 boys and 5 girls), Mohan wanted to invite friends for picnic. If there have to be exactly 3 girls in invites, then the number of ways in which he can invite them are,
- a)320
- b)80
- c)160
- d)200
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
From his 9 friends (4 boys and 5 girls), Mohan wanted to invite friend...
Three girls can be selected from 5 girls in 5C3 ways. As number of boys to be invited is not given, hence out of 4 boys he can invite them in 24 ways, so total of
24 X 5C3 ways = 16 X 
=160 ways
=160 waysMost Upvoted Answer
From his 9 friends (4 boys and 5 girls), Mohan wanted to invite friend...
To determine the number of ways Mohan can invite 3 girls from his 9 friends (4 boys and 5 girls), we can use the concept of combinations.
Combination formula:
The number of ways to choose r items from a set of n items is given by the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n! denotes the factorial of n, which is the product of all positive integers less than or equal to n.
Number of ways to invite 3 girls:
In this case, Mohan needs to invite exactly 3 girls. Therefore, r = 3.
Since there are 5 girls in total, n = 5.
Plugging in these values into the combination formula, we get:
C(5, 3) = 5! / (3! * (5-3)!)
= 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2 * 1)
= (5 * 4) / (2 * 1)
= 10
So there are 10 different ways to invite 3 girls from the group.
Number of ways to invite the remaining friends:
After selecting the 3 girls, Mohan needs to invite the remaining friends. Since there are 4 boys and 2 remaining spots, he can choose any combination of boys.
The number of ways to select 2 boys from a group of 4 is given by:
C(4, 2) = 4! / (2! * (4-2)!)
= 4! / (2! * 2!)
= (4 * 3 * 2!) / (2! * 2 * 1)
= (4 * 3) / (2 * 1)
= 6
Total number of ways to invite friends:
To calculate the total number of ways to invite friends, we multiply the number of ways to choose 3 girls by the number of ways to choose 2 boys:
Total ways = 10 * 6 = 60
Therefore, the number of ways Mohan can invite friends for the picnic with exactly 3 girls is 60.
Combination formula:
The number of ways to choose r items from a set of n items is given by the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Where n! denotes the factorial of n, which is the product of all positive integers less than or equal to n.
Number of ways to invite 3 girls:
In this case, Mohan needs to invite exactly 3 girls. Therefore, r = 3.
Since there are 5 girls in total, n = 5.
Plugging in these values into the combination formula, we get:
C(5, 3) = 5! / (3! * (5-3)!)
= 5! / (3! * 2!)
= (5 * 4 * 3!) / (3! * 2 * 1)
= (5 * 4) / (2 * 1)
= 10
So there are 10 different ways to invite 3 girls from the group.
Number of ways to invite the remaining friends:
After selecting the 3 girls, Mohan needs to invite the remaining friends. Since there are 4 boys and 2 remaining spots, he can choose any combination of boys.
The number of ways to select 2 boys from a group of 4 is given by:
C(4, 2) = 4! / (2! * (4-2)!)
= 4! / (2! * 2!)
= (4 * 3 * 2!) / (2! * 2 * 1)
= (4 * 3) / (2 * 1)
= 6
Total number of ways to invite friends:
To calculate the total number of ways to invite friends, we multiply the number of ways to choose 3 girls by the number of ways to choose 2 boys:
Total ways = 10 * 6 = 60
Therefore, the number of ways Mohan can invite friends for the picnic with exactly 3 girls is 60.
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From his 9 friends (4 boys and 5 girls), Mohan wanted to invite friends for picnic. If there have to be exactly 3 girls in invites, then the number of ways in which he can invite them are,a)320b)80c)160d)200Correct answer is option 'C'. Can you explain this answer?
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