# A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is Option 1) 196 Option 2) 280 Option 3) 346 Option 4) 140

As we learnt in

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

$^{n}c_{r}=\frac{(n)!}{r!(n-r)!}$

- wherein

Where $1\leq r\leq n$

Choose 10 out of 13 questions and choose at least 4 out of first five.

Choices $=^{5}C_{4}\times^{8}C_{6}=\frac{5\times 8\times 7}{2}=140$  and  $=^{5}C_{5}\times^{8}C_{5}=\frac{8\times 7\times 6}{6}=56$

Total = 196

Correct option is 1.

Option 1)

196

This is the correct option.

Option 2)

280

This is an incorrect option.

Option 3)

346

This is an incorrect option.

Option 4)

140

This is an incorrect option.

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