3. Solve the following problems (a) There are 20 bags labeled from 1 to 20. From

Question

3. Solve the following problems

(a) There are 20 bags labeled from 1 to 20. From each bag we take out either a blue ball or a red ball. We get 5 points for each blue ball, and 8 points for each red ball. What is the number of outcomes where we end up with 145 points? (Find the value)

(b) Mcnuggets can be purchased in 9 or 12 or 20 packs. What CAN YOU SAY about the number of ways to purchase a total of 1000 mcnuggets when the order of the purchase matters? What CAN YOU SAY about the number of ways to purchase a total of 1000 mcnuggets when the order of the purchase does not matter?

(d) Find the number ways to distribute 10000 pebbles to 3 students (Scott, Cora, Liam) such that:

- Cora gets at most 15 pebbles, but in multiples of 5.

- Liam gets multiple of 20

- Scott gets a multiple of 5

Explanation / Answer

As per Chegg policy, I am solving queston 1. Please post other questions seperately :)

Solving the equations to get the no. of red and blue balls,

r+b = 20

5b+8r = 145

we get b = 5 and r=15

Now we wind the no. of ways in which we can pick 5 blue balls and 15 red balls from the 20 bags.

This is equal to the no. of ways of picking 5 bags (blue ) from 20 bags.

Hence, the answer is 20 C5 = 20*19*18*17*16 / [1*2*3*4*5] = 15504 ways

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