4. [-/2 Points] DETAILS EPPDISCMATH5 9.2.015. MY NOTES ASK YOUR TEACHER Suppose a certain combination lock requires three selections of numbers, each from 1 through 25. (a) How many different combinations are possible? (b) Suppose the locks are constructed in such a way that no number may be used twice. How many different combinations are possible? Show My Work (Optional)@ 5. [-/1 Points] DETAILS EPPDISCMATH5 9.4.017. MY NOTES ASK YOUR TEACHER What is the minimum number of integers that must be picked in order to be sure that at least two of them have the same remainder when divided by 5? # Show My Work (Optional)@ 6. [-/4 Points] DETAILS EPPDISCMATH5 9.6.017. MY NOTES ASK YOUR TEACHER (a) A store sells 8 colors of balloons with at least 32 of each color. How many different combinations of 32 balloons can be chosen? Apply the method of Example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 32 balloons that can be chosen is (b) If the store has only 12 red balloons but at least 32 of each other color of balloon, how many combinations of balloons can be chosen? Use the method of Example 9.6.2(c) to answer this question. If the store has only 12 red balloons, then the number of different selections of 32 balloons of the different colors is the same as the number of different selections that contain 12 or fewer red balloons. Let 7 be the set of all possible selections, assuming that there are at least 32 balloons of each type, let Ryo be the set of selections in 7 that contain 12 or fewer red balloons, and let R be the set of selections from 7 that contain 13 or more red balloons. Use the relationships among R 21 R. , and T to find that the number of different combinations of 32 balloons that can be chosen is (c) If the store has only 8 blue balloons but at least 32 of each other color of balloon, how many combinations of balloons can be chosen? (d) If the store has only 12 red balloons and only 8 blue balloons but at least 32 of each other color of balloon, how many combinations of balloons can be chosen?7. [-/1 Points] DETAILS EPPDISCMATH5 9.7.011. The row of Pascal's triangle that corresponds to n = 10 is as follows. 1 10 45 120 210 252 210 120 45 10 1. What is the row that corresponds to n = 11? (Enter the row in the correct order as a comma-separated list.) # Show My Work (Optional)@) 8. [-/5 Points] DETAILS EPPDISCMATH5 9.7.022. Use the binomial theorem to expand the following expression. (u - V) By the binomial theorem with 5 in place of n, (a + b)5 = 25 +[ atb + 108 7)=263 + 5264 + 65. Now (u - v)5 = (u + (-v))". Substituting u in place of a and -v in place of b gives that (u - v)' Show My Work (Optional)?) 9. [-/1 Points] DETAILS EPPDISCMATH5 9.7.032. Find the coefficient of u v 2 when the following expression is expanded by the binomial theorem. 18v12 in (u2 - v2)10