Question

1) A candy store sells five different flavors of jelly beans. In how many way can we fill a bag with 100 jelly beans

2) How nay ternanry strings ( consisting of 0s, 1s and 2s) of length 20 can be formed if at least one of the last three digits must be a 1

Answer #1

**1)**

We want 100 jelly beans in the bag, and in all 5 flavors are there with us. So every time we have 5 options to pick from for each of the hundred jelly beans to be put in the bag.

**Thus the total number of ways= 5*5*5*.......(100 times)
= 5 ^{100} =7.88860905e69**

**2)**

We have three options 0,1 and 2 for the strings.

Now the total number of ways to form 20 length string=
3*3*3...(20 times) = 3^{20}

The total number of ways to form 20 length string with no 1's in
it (i.e. 2 options are left at each place) = 2*2*2... (20 times)=
2^{20}

Thus the total ways to form 20 length string with at least one digit being 1 =

total number of ways to form 20 length string- The total number of ways to form 20 length string with no 1's in it

= = 3485735825

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