There are 10 candidates for an examination out of which 4 are appearing in Mathematics and remaining 6 are appearing indifferent subjects. In how many ways can they be seated in a row so that no two Mathematics candidates are together?

Explanation

In this method first arrange the remaining candidates
Here, remaining candidates=6
`"X0X0X0X0X0X0X"`
X:Places available for Mathematics condidates
0:Places for others
remining candidates can be arranged in 6! Ways. There are seven places available for mathematics candidates so that no two mathematics candidates are together. now, four candidates can be placed in these sevenn places
in `.^(7)P_(4)` ways.
Hence, the total number of ways`=6!xx.^(7)P_(4)=720xx840`
`=604800`