In a conference 10 speakers are present. If `S_1` wants to speak before `S_2a n dS_2` wants to speak after `S_3,` then find the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number.

Explanation

According to question the order of speakers `S_(1),S_(2), " and" S_(3)` can be (not necessarily consecutive)
`S_(1)S_(3)S_(2) " or" S_(3)S_(1)S_(2)`
For each order we can select 3 slots out of 10 in `.^(10)C_(3)` ways.
After selecting these three slots in which speakers `S_(1),S_(2),S_(3)` have two ways of arrangement, the remaining seven speakers can be arranged in the remaining seven slots in 7! ways.
Hence, total number of arrangements `=2 .^(10)C_(3)7!`