Question

Evaluate C(11,4). C(11,4) equals =

Six cards are marked with the numbers 1, 2, 3, 4, 5, and 6 , then shuffled, and three cards are drawn.

a. How many different three -card combinations are possible?

b. How many three -card hands contain a number less than three?

Use a tree diagram for the following. a. Find the number of ways 2 letters can be chosen from the set {U, V, W, X} 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?

How many different committees can be formed from 8 teachers and 33 students if the committee consists of 2 teachers and 4 students? In how many ways can the committee of 6 members be selected?__

In a game of musical chairs, 5 children will sit in 4 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? Is this problem a permutation or a combination?

Marbles are being drawn without replacement from a bag containing 10 marbles. First, decide whether this situation involves permutations or combinations. Then, in the following cases, determine the possible number of samples that can be drawn. Does this problem use combinations or permutations?

An urn contains 7 white balls and 9 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 16 balls: (a) If 2 balls are white and 1 is red? (b) If all 3 balls are white? (c) If all 3 balls are red?

From a group of 8 newly hired office assistants, 3 are selected. Each of these 3 assistants will be assigned to a different manager. In how many ways can they be selected and assigned? The office assistants can be selected and assigned in __ different ways.

A group of 22 workers decides to send a delegation of 6 to their supervisor to discuss their work assignments. In the following cases, determine the possible number of delegations. The number of possible 6 -person delegations is __ .

A company sells regular hamburgers as well as a larger burger. Either type can include cheese, relish, lettuce, tomato, mustard, or ketchup. a. How many different hamburgers can be ordered with exactly 3 extras? b. How many different regular hamburgers can be made that use any 3 of the extras? c. How many different regular hamburgers can be ordered with at least 2 extras?

Jeanine Baker makes floral arrangements. She has 14 different cut flowers and plans to use 6 of them. How many different selections of the 6 flowers are possible? How many ways can the 6 flowers be chosen?

Answer 1