statistics and Probability

Suppose that 3 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 3 are hearts? A bag contains 5 red apples and 3 yellow apples. 3 apples are selected at random. Find the probability of selecting 1 red apple and 2 yellow apples. 3 A bag contains 6 red balls and 4 blue balls. If 3 balls are selected at random, find the probability of selecting 3 red balls A group of 8 workers decides to send a delegation of 3 to their supervisor to discuss their grievances. Complete parts a) through (c) below. (a) How many delegations are possible? (b) If it is decided that a particular worker must be in the delegation, how many different delegations are possible? In a game of musical chairs, 7 children will sit in 6 chairs arranged in a row (one will be left out). In how many ways can this happen if we count rearrangements of the children in the chairs as different outcomes? Does this problem involve permutations, combinations, or neither? Use a tree diagram for the following. . Find the number of ways 2 letters can be choosen from the set {D, E, F, G) if order is important and repetition is allowed. b. Reconsider part a if no repeats are allowed. c. Find the number of combinations of 4 elements taken 2 at a time. Does this answer differ from part a or b? Nine cards are marked with the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, then shuffled, and three cards are drawn. . How many different 3-card combinations are possible? b. How many 3-card hands contain a number less than three? Evaluate the combination. Do C(9,3) Kristen's financial advisor has given her a list of 11 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this? Find the number of distinguishable permutations of the letters in each word below. (a) greater (b) Hollywood (c) referred A couple has narrowed down the choices of a name for their new baby to 4 first names and 7 middle names. How many different first- and middle-name arrangements are possible? Evaluate the permutation. P(n, 1)