Eight people go to the theatre and sit in a particular group of eight adjacent reserved seats in the

Question

Eight people go to the theatre and sit in a particular group of eight adjacent reserved seats in the front row. Three of the eight belong to one family and sit together. If the other five people do not mind where they sit, find the number of possible seating arrangements for all eight people.[4] If the other five people do not mind where they sit, except that two of them refuse to sit together, find the number of possible seating arrangements for all eight people.[5] The salad bar at a restaurant has $6$ separate bowls containing lettuce, tomatoes, cucumber, radishes, spring onions, and beetroot respectively. John decides to visit the salad bar and make a selection. At each bowl, he can choose to take some of the contents or not. Assuming that John takes some of the contents from at least one bowl, find how many different selections he can make.[2] John decides he is going to have $4$ salad items, and one of them will be tomatoes. How many different selections can he make?[1]

Accepted Answer

(a)(i) $4320$ (a)(ii) $2880$ (b)(i) $63$ (b)(ii) $10$

RI Permutation and Combination Tutorial Q10

RI Permutation and Combination Tutorial Q10

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