Question

A restaurant offers a meal combo that consists of a beverage, a main course, and a dessert. There are 5 beverages, 6 main courses, and 4 desserts. How many meal combos are available?

20

30

15

120

A coin is tossed 12 times. What is the number of ways the coin can land with 6 heads and 6 tails?

P(12,6)

P(12,6)*P(12,6)

12!/(6!*6!)

C(12,6)*C(12,6)

Answer 1

FIRST QUESTION:

A meal combo consists of a beverage, a main course, and a dessert.    
A beverage can be selected in 5 ways   
A main courses can be selected in 6 ways         
A dessert can be selected in 4 ways      

Thus number of different combo means = 5x6x4 = 120

SECOND QUESTION:

When a coin is tossed 12 times and number of heads are 6, these 6 heads can be at any 6 positions out of 12 and remaining 6 positions will be Tails.

So we have to select 6 positions out of 12, where heads appear, this can be done in C(12, 6) ways. And we do not need to select positions for tails as remaining 6 will be tails only.

Thus the number of ways = C(12, 6) = 12!/(6!*6!)