Question

Ten guests are to be seated in a row. Three of them are to be seated together. Out of the remaining 7 ,two do not wish
to sit side by side. Find the number of possible arrangements.​

Answer 1

Since 3 of the 7 students must be seated together they can be treated as 1 unit, and within that unit they can be seated in 3! = 3*2*1 = 6 ways. Along with the other 4 students (each treated as 1 unit), the 5 units can be arranged in 5! = 5*4*3*2*1 = 120 ways.