Solving Problems That Involve Combinations

How many 6-member committees can be formed from 8 girls and 9 boys if (show steps)

a.there are no conditions

b.there must be exactly 3 girls

c.there must be at least 4 boys

Solving Probability Problems That Involve Permutations and Combinations

A person has bought one ticket each for two separate lotteries. Determine the probability of winning a grand prize for the two lotteries. (show all the steps)

a.For the first lottery, 5 random numbers are drawn from 40. To win the grand prize, you need to select the correct 5 numbers.

b.For the second lottery, 4 random numbers are drawn one at a time from 35. To win the grand prize, you need to select the correct 4 numbers in the correct order.

c.A person is more likely to win the first lottery described in question 1.a., even though the first lottery requires a person to have more correct numbers (5 compared to 4) selected from a larger set of numbers (40 compared to 35). Explain why this is true

solve each probability questions

a.The letters T, C and A are placed in a bag. If a student randomly draws the three letters out, what is the probability that they are drawn in order to spell CAT?

b.A student can make a 3 digit computer password from the numbers 0 to 9. If the digits cannot be repeated, what is the probability of someone guessing the correct password?

c.The padlock on a gym locker consists of any 3 numbers from 1 to 60. If the numbers can repeat, what is the probability a student can guess the code on their first try?

d.Daniel, Amy, and Brad are 3 of the 10 finalists in a singing competition. What is the probability that Daniel, Amy, and Brad will place first, second, and third, in any order?

e.Three students are being selected from a class of 10 to be on a specialcommittee. If Tracy, Sydney, and Sam are in the class, what is the probability that they are selected?

f.The letters of the word ALGORITHMS are placed in a bag, and a student draws 3 letters. What is the probability that the letters selected are 1 vowel and 2 consonants?

g.A student is planning a backpacking trip to Europe, where she will visit 7 countries. If there are 10 countries to choose, what is the probability that three of the countries will be France, Germany, and Italy?

h. The coach of a 10 player handball team has to pick 7 players to be in the starting lineup. If Devyn is on the team, what is the probability that he will be on the starting lineup?

3. A standard deck of 52 cards consists of 4 suits (hearts, clubs, diamonds, and spades). If a student deals 3 cards from a standard deck, determine the probability to the nearest hundredth, that at least one card is a heart. You may use either direct or indirect reasoning