PLSS HELP!! VERY EASY. Alex wants to invite 5 of his 9 friends to his birthday party. Two of his friends are twins and they agree to come only if they are invited together, hence Alex will either invite both or neither of them. In how many ways can Alex invite five of his friends?

35 ways

Step-by-step explanation:

Alex has 9 friends and wants to invite 5 friends. Since Alex requires two of his friends who are twins to come together to his birthday party, since the two of them form a group, the number of ways we can select the two of them to form a group of two is ²C₂ = 1 way.

Since we have removed two out of the nine friends, we are left with 7 friends. Also, two friends are already selected, so we are left with space for 3 friends. So, the number of ways we can select a group of 3 friends out of 7 is ⁷C₃ = 7 × 6 × 5/3! = 35 ways.

So, the total number ways we can select 5 friend out of 9 to  party come to the birthday include two friends is  ²C₂ × ⁷C₃ = 1 × 35 = 35 ways

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