Question

# A student is to answer $$10$$ out of $$13$$ questions in an examination such that he must choose at least 4 from first five questions. The number of choices available to him is

A
196
B
280
C
346
D
140

Solution

## The correct option is B $$196$$The number of choices available to him is$$\displaystyle{ }^{ 5 }{ { C }_{ 9 } }\times { }^{ 8 }{ { C }_{ 6 } }+{ }^{ 5 }{ { C }_{ 5 } }\times { }^{ 8 }{ { C }_{ 5 } }$$$$\displaystyle=\frac { 5! }{ 4! \, 1! } \times \frac { 8! }{ 6!\, 2! } +\frac { 5! }{ 5!\, 6! } \times \frac { 8! }{ 5!\, 3! }$$$$\displaystyle=5\times\frac { 8\times 7 }{ 2 } +1\times \frac { 8\times 7\times 6 }{ 3\times 2 }$$$$\displaystyle =5\times 4\times 7+8\times 7$$$$=140+56$$$$=196$$Maths

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