1. A Boy found a bicycle lock for which thecombination was unknown. The correct

Question

   1. A Boy found a bicycle lock for which thecombination was unknown. The correct combination is afour-digit number,d1d2d3d4, wheredi, i = 1,2,3,4, is selected from 1,2,3,4,5,6,7, and 8.How many different lock combinations are possible with such alock?    2. The "eating club" is hosting amake-your-own sundae at which the following are provided:
a) How many sundaes are possible using one flavor of icecream and three different toppings? b) How many sundaes are possible using one flavor ofice cream and from zero to six toppings? c) How many different combinations of flavors of threescoops of ice cream are possible if itis      permissible to make all threescoops the same flavor.?

Explanation / Answer

Q1) we can fill each digit in 8 different ways and they are allindependent. Hence we can have a total of 8*8*8*8 = 4096 lockcombinations.

Q2)

a)      Ways to select one flavor = 4C1 =4

Ways to select 3 toppings out of 6 = 6c3 = 20.

Hence total number of sundaes possible =4*20 = 80

b)      Ways to select one flavor = 4C1 =4

Since we can have any number of toppings we have a choice toeither add the topping or not. Hence each topping can be dealt within 2 ways. So there is a total of 2*2*2*2*2*2 = 64 ways of puttingtoppings.

Hence total number of ways = 4*64 = 256

c)       We can put first scoop from4 in 4 ways. Second one can also be put in 4 ways and third one canalso be put in 4 ways. So total # of ways of putting 3 scoops =4*4*4 = 64 ways

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