The probability of inviting three friends on 5 consecutive days, exactly one friend a day and no friend is invited on more than two days is

Step-by-step solution

There are 3 friends and 5 days. Each day, one friend is invited, so there are 3^5 = 243 total ways to invite friends. Let the friends be A, B, C . We need to count the number of ways such that each friend is invited at most twice. Since there are 5 days, the possible distributions of the number of days each friend is invited are (2, 2, 1) in some order. The number of ways to choose which friend is invited once is ³C₁ = 3 . For a specific distribution, say A is invited 1 time, B is invited 2 times, and C is invited