NIMCET 2014 — Mathematics PYQ

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Question

NIMCET 2014 — Mathematics PYQ

NIMCET | Mathematics | 2014

There are $8$ students appearing in an examination of which $3$ have to appear in Mathematics paper and the remaining $5$ in different subjects. Then, the number of ways they can be made to sit in a row, if the candidates in Mathematics cannot sit next to each other is:

Choose the correct answer:

Explanation

Calculation:

Given: $8$ students appearing in an examination of which $3$ have to appear in Mathematics paper and the remaining $5$ in different subjects.

There are $5$ candidates not appearing in mathematics.

Let us arrange these $5$ in a row, each shown by $X$ .

They can be arranged in $5! = 120$ ways.

On both sides of each $X$ , we put an $M$ , as shown below:

M X M X M X M X M X M

Now, $3$ candidates in mathematics can be arranged at $6$ places in $^{6}P_{3}$ ways:

^{6}P_{3} = \frac{6!}{(6-3)!} = 6 \times 5 \times 4 = 120 \text{ ways}

Hence, the total number of arrangements:

\text{Total ways} = 120 \times 120 = 14400