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There are x number of identical balls which are to be placed in y number of distinct buckets. If x>= ky (where k is a natural number greater than equal to 1), then in how many ways can you place the balls in the bucket with the condition that each bucket should contain at least k balls?
  • a)
    (x-k) C (y-1)
  • b)
    (x-1) C (y-k)
  • c)
    (x-ky+y-1) C (y-1)
  • d)
    (x-ky+y+k-2) C (y-k)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
There are x number of identical balls which are to be placed in y numb...
As there have to be at least k balls in each bag, so firstly put k balls in each bag i.e k*y balls. Balls remaining: x-ky
We can now apply balls and sticks method.
y bags= y variables, they need to equal to x-k*y, no restrictions on how many balls in each bag. We can make a equation out of this:
a1 + a2 + ... + ay = x- k*y
On solving it we get our answer:  (x-ky+y-1) C (y-1)
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Most Upvoted Answer
There are x number of identical balls which are to be placed in y numb...
Is less than or equal to y, then each bucket can have at least one ball and there may be some empty buckets.
If x is greater than y, then there will be at least one bucket with more than one ball, and there may be some empty buckets.
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There are x number of identical balls which are to be placed in y number of distinct buckets. If x>= ky (where k is a natural number greater than equal to 1), then in how many ways can you place the balls in the bucket with the condition that each bucket should contain at least k balls?a)(x-k) C (y-1)b)(x-1) C (y-k)c)(x-ky+y-1) C (y-1)d)(x-ky+y+k-2) C (y-k)Correct answer is option 'C'. Can you explain this answer?
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