1
Question
In how many ways can 20 oranges be given to four children where each should get at least one orange?
In how many ways can 20 oranges be given to four children where each should get at least one orange?
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Solution
The correct option is B 969
The problem is equivalent to number of non-negative integral solutions of x1+x2+...+xr=n is n+r−1Cr−1.
Since every student should get atleast 1 orange
After giving 1 orange to each student, 16 oranges are left to be distributed
Thus the problem is equivalent to finding the number of integral solutions for x1+x2+x3+x4=16
and n=16;r=4
no. of ways = no. of integral solution = n+r−1Cr−1=19C3=969
The problem is equivalent to number of non-negative integral solutions of x1+x2+...+xr=n is n+r−1Cr−1.
Since every student should get atleast 1 orange
After giving 1 orange to each student, 16 oranges are left to be distributed
Thus the problem is equivalent to finding the number of integral solutions for
x1+x2+x3+x4=16
and n=16;r=4
no. of ways = no. of integral solution = n+r−1Cr−1=19C3=969
and n=16;r=4
no. of ways = no. of integral solution = n+r−1Cr−1=19C3=969
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