15 points 5. You have one box with 3 white balls and 3 red balls, and you random

Question

15 points 5. You have one box with 3 white balls and 3 red balls, and you randomly keep picking balls without replacement. If X is a random variable representing the number of trials required for the 1st red ball, what is the probability mass function of X? 20 points 6. There are seven pictures on display in a line. Four of them are portraits, one is a painting, and the remaining are photos. If pictures of the same kind need to be arranged together, what is the number of ways that we can put these seven pictures in a line?

Explanation / Answer

As per the chegg policy, we are advised to do one problem at a time so i am attemtping the 6th one.

6. We need to arrange pictures of same kind together so the number of ways of arranging Portraits, painting & photo

= 3! = 6

Now Potraits can be arranged within themselves with 4! i.e. 24 ways

And Photos can be arranged within themselves with 2! i.e. 2 ways

Hence,

Total number of ways by which these seven pictures can be in a line = 6*24*2 = 288

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