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Question

The total number of ways in which a beggar can be given at least one rupee from two 1 rupee coins, three 50 paisa coins and four 25 paisa coins is

A
51
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B
52
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C
53
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D
54
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Solution

The correct option is D 54
Let the beggar be given x number of one rupee coins, y number of 50 paisa coins and z number of 25 paisa coins.

x+0.5y+0.25z1
where x=0,1,2; y=0,1,2,3; z=0,1,2,3,4
4x+2y+z4

For x=1,2, y and z can take any value.
Number of ways =2×4×5=40

For x=0,2y+z4

For y=0,z=41 way
For y=1,z{2,3,4}3 ways
For y=2,z{0,1,2,3,4}5 ways
For y=3,z{0,1,2,3,4}5 ways

Total number of ways =40+1+3+5+5=54

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