+586 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.
