Chris makes a smoothie for breakfast every day. When he makes smoothies with bananas, the distribution of calories is skewed right with a mean of 248.6 and a standard deviation of 39.1. His berry smoothies have a distribution of calories that is approximately Normal with a mean of 279.1 calories and a standard deviation of 60.8. Random samples of 35 of each type of smoothie are selected. What is the probability of the banana smoothies having fewer mean calories than the berry smoothies?

34

Step-by-step explanation:

0.9937

Step-by-step explanation:

Combinations allow 10,000, permutations allow 5,040.

Step-by-step explanation:

If we allow for repetition, we can have 10^4 possible combinations, if we can start numbers with 0. This is a base 10 system with 4 different objects.

If we don't allow for repetition, we will have 10 possible objects and a subset of 4. Every time we use a digit, we cannot reuse it, so we first have 10 possible digits for the 1st digit.

We have 10*9*8*7 possible combinations if we were to fill in the rest.

0XXX

Since we chose 0, we have 9 other digits remaining (9*8*7 possible permutations)

01XX

8 other digits. (8*7 possible permutations in this system)

018X

7 digits are possible now. (7 possible permutations if we pick 1 more digit)

In conclusion, we would have 10*9*8*7 (10!/6! or 5040) possible permutations in this system. Compared to using combinations where order and reuse is allowed, we have 10^4 possible combinations, or 10000. Combinations win.