Seating in a Movie Theater How many different ways can 5 people-A, B, C, D, and E-sit in a row at a movie theater if (a) A and B must sit together; (b) C must sit to the right of, but not necessarily next to, B; (c) D and E will not sit next to each other?

How many different meals can occur when there are 10 different salads, 23 different deserts, and 5 main dishes. You can choose one main dish one salad and two deserts – no duplication on the deserts.

3: At a Chinese restaurant, dinner for 8 people consists of 3 items from column A, 4 items from column B and 3 items from column C. If columns A, B and C have 5, 7 and 6 items respectively how many different dinner combinations are possible?

MAT 271 -PRACTICE EXERCISE li 1. A landscaper has 4 mangos, 3 oranges and 2 grape trees to be planted in a row. How many different arrangements can be made? 2. In how many ways can a committee of 7 members be selected from 10 boys and 12 girls such that (i). There are at least 4 girls. (ii). There are at most 2 boys. (ii) The committee has at least 2 girls and not less than 3 boys. 3. A card is picked at random from a ordinary deck of 52 cards. Find the probability that the card is either club or ace. 4. If two fair dice are tossed, what is the probability that their sum is less than or equal to 5, given that at least one face shows a 2? 5. Let A and B be two events associated with an experiment, and suppose P(A)=0.5 and P(AUB)=0.8. Let P(B) = p. For which values of pare: (a) A and B independent? (b) A and B mutually exclusive? 6. A card is drawn from a standard deck of 52 cards and then a second is drawn without replacing the first card. If we know that the second card is a spade,…

Part A,B and C please.