1 A resturant is offering a daily special entree with select

1) A resturant is offering a daily special entree with selection of 1 appetizer, 1 side dish and 1 desert. There are 4 appetizers, 5 side dishes and 2 deserts on the menu.

a) In how many ways can a customer select an appetizer, a side dish and a desert?

b) In how may ways a customer can place his order, if he may choose to option out appetizer , side dish or desert?

2) In how many ways can three boys and three girls be seated in row , if boys are required to seat in the alternate chairs?

3) In how many ways can three boys and three girls be seated in row so that at most two boys can sit together ?

Solution

4 appetizers, 5 side dishes and 2 deserts

a) For each appetizer and 1 side dish we have 2 deserts.

Hence total ways = 4(5)(2) = 40

b) 3 boys and 3 girls

Let 3 girls be seated first in 3! ways

Then boys have places including both ends 4 so that they occupy alternate places.

No of ways 3 boys can occupy 4 places is 4c3

Henc3 total = 4(3!) = 24

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3) atmost 2 boys sit together

This is equal to total ways - all 3 boys sit together

Total ways = 6!

All 3 boys sit together = 4!(3!) = 144 ways

(3 boys together taken one unit and there are 4 units including 3 girls. 3 boys among themselves can be arranged in 3! ways)

Hence no of ways atmost 2 boys sit together = 6! -144 = 720-144

= 576 ways.