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# Counting And Probability Questions

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1. Find the number of 10-digit numbers where the sum of the digits is divisible by 5.

2.We say that a quadrilateral is a bow-tie if two of the sides cross each other. An example is shown below.

Seven different points are chosen on a circle. We draw all \(\binom{7}{2} = 21\) chords that connect two of these points. Four of these 21 chords are selected at random. What is the probability that the four chords form a bow-tie quadrilateral?

3. I have a bag with 5 pennies and 6 nickels. I draw coins out one at a time at random. What is the probability that after 4 draws I have removed no more than 2 pennies from the bag?

4. The Bad News Bears are playing against the Houston Toros in a baseball tournament. The first team to win three games wins the tournament. The Bears have a probability of 2/3 of winning each game. Find the probability that the Bears win the tournament.

Nov 4, 2019

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2. The answer is 2/399.

3. The answer is 13/33.

Nov 4, 2019
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1. I think the answer is 10,000,000.

4. It's (2/3)^3 = 8/27.

Nov 5, 2019
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Do not put a string of questions like this.

We are not here to do all your homework.

Nov 7, 2019
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Now that you have drawn my attention to you, I can also see that you have NEVER said thankyou to anyone here.

Nor have you ever interacted with anyone in order to learn anything.

Your icon may be cute but you certainly are not.

Melody  Nov 7, 2019
edited by Melody  Nov 7, 2019