1.

In an examination, there are 8 candidates out of which 3 candidates have to appear in mathematics and the rest in different subject. In how many ways can they be seated in a row, if candidtes appearing in mathematics are not to sit together ?

Answer» Correct Answer - 14400
Clearly, 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:
MXMXMXMXMXM
Now, 3 candidates in mathematics can be arrnged at 6 places in ` ""^(6)P_(3) " ways "=(6xx5xx4) " ways " =120` ways.
Total number of arrangements `=(120 xx 120)=14400.`


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