Gordon buys 5 dolls for his 5 niece . The gifts include 2 identical Sun and Fun beach dolls , one Elegant eddie dress doll , one GI jose doll , and one tulip troll doll . If th eyoungest niece doesnot want the GI jose doll , in how many different ways can he give the gifts?
OA 48
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Deepthi Subbu
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Rahul@gurome
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Required number of ways = Number of ways 5 dolls can be distributed among 5 nieces - Number of ways in which youngest one gets the GI Joe dollDeepthi Subbu wrote:Gordon buys 5 dolls for his 5 niece . The gifts include 2 identical Sun and Fun beach dolls , one Elegant eddie dress doll , one GI jose doll , and one tulip troll doll . If th eyoungest niece doesnot want the GI jose doll , in how many different ways can he give the gifts?
OA 48
Number of ways 5 dolls can be distributed among 5 nieces = 5! = 120
As there are 2 dolls of same kind, effective number of ways = 120/2 = 60
Number of ways in which youngest one gets the GI Joe doll = Number of ways to distribute other 4 dolls among remaining 4 nieces = 4!/2 = 12 (Division by 2 for the same reason as above)
Required number of ways = 60 - 12 = 48
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rishab1988
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Although Rahul has solved this question.I solved in a direct way.
There are 5 dolls and 5 girls. 2 dolls are same.
One of the girls doesn't get a specific doll (G.I Joe doll).
Lets make 5 dashes _ _ _ _ _ (for 5 girls).
We fill the dash with the most restriction first.Since the smallest girl can't be alloted one of the dolls,she can only be alloted one of the 4 remaining dolls.
4 _ _ _ _
Now the second girl can be alloted any of the 4 remaining dolls [ one of the 5 dolls has already been alotted]
4 4 _ _ _
Similarly the third girl can be alloted any of the 3 reaming ones.
4 4 3 _ _
This is same procedure is repeated fot the 2 other girls
4 4 3 2 1.
Now don't forget that the question mentions that 2 of the dolls are identical. So divide by 2!.If 3 dolls were identical ,we would have divided by 3!.
(4*4*3*2*1)/2!=4*4*3=48.
This question was all about logic.I solved it 2 steps.
There are 5 dolls and 5 girls. 2 dolls are same.
One of the girls doesn't get a specific doll (G.I Joe doll).
Lets make 5 dashes _ _ _ _ _ (for 5 girls).
We fill the dash with the most restriction first.Since the smallest girl can't be alloted one of the dolls,she can only be alloted one of the 4 remaining dolls.
4 _ _ _ _
Now the second girl can be alloted any of the 4 remaining dolls [ one of the 5 dolls has already been alotted]
4 4 _ _ _
Similarly the third girl can be alloted any of the 3 reaming ones.
4 4 3 _ _
This is same procedure is repeated fot the 2 other girls
4 4 3 2 1.
Now don't forget that the question mentions that 2 of the dolls are identical. So divide by 2!.If 3 dolls were identical ,we would have divided by 3!.
(4*4*3*2*1)/2!=4*4*3=48.
This question was all about logic.I solved it 2 steps.
