Five students are to be arranged on five chairs for a photograph. Three of these are girls and the rest are boys. Find out the number of ways in which all three girls do not occupy consecutive seats.

As per the question, three girls can’t occupy consecutive seats but two can.

Therefore, if we find the number of ways in which all three girls occupy consecutive seats and subtract this number from the total number of ways in which the five people can be arranged among themselves, we will get the required answer.

5 students can be arranged among themselves in ⁵p₅ ways = 120 ways.

Assume that the 3 girls are one entity. The total number of ways in which they can be arranged among themselves = 3! = 6
Also, the set of three girls and the other students can be arranged among themselves in 3! = 6 ways.
Thus, the total number of ways in which three girls are together = 6 × 6 = 36

Thus, a number of ways in which all 3 girls will not occupy consecutive seats = 120 – 36 = 84.