Permutations and Combinations - Statistics

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This quiz has been taken 23 times
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The average score is 5 of 21

Answer Stats

Question	Answer	% Correct
Peter is packing his pencil case. He must pack 3 distinct pencils, 2 distinct erasers, and 2 distinct markers in some order. However, he will not put an item in his case if there are already more of that type of item than any other type of item. (Eg. Peter will not put another pencil in his case if there are already more pencils than markers or more pencils than erasers in the case). How many different orders are there for Peter to put items in his case?	864	59%
The number of ways of arranging n objects in a line is	n!	53%
The number of ways of arranging n objects in a circle where rotations of the same arrangement aren’t considered distinct is	(n-1)!	41%
The number of ways to arrange k objects out of n total objects is		35%
The number of ways of arranging n objects in a circle where rotations of the same arrangement aren’t considered distinct and reflections of the same arrangement aren’t considered distinct is	(n-1)!/2	35%
Gauss, Pauli, Einstein, Newton, Edison, and Faraday are sitting at a circular table. Einstein, Newton, and Faraday are enemies so they refuse to sit next to each other. With this condition, how many ways are there for the 6 physicists to sit at the table if rotations are not counted as distinct orientations?	12	29%
How many 4 digit numbers exist such that the first digit is odd and the other 3 digits are even and all digits distinct?	300	29%
How many 6 digit numbers exist such that all the digits are distinct, and it’s first 2 digits are 6 or more, the last 2 digits are 5 or less, and the 3rd digit is a nonzero multiple of 7?	900	24%
The number of ways to choose k objects out of n total objects is:		18%
True or False?		18%
How many ways are there to rearrange the letters in COMPUTER such that the C, O, M, and P stay together (not necessarily in the same order)?	2880	18%
Usually, the words ”permute”, ”order does matter”, etc. imply a __________ while the words ”choose”, ”select”, ”order doesn’t matter”, etc. imply a __________.	Permutation, Combination	18%
The number of ways to order a word is		12%
You have 12 different energy bars that you need to give to 3 people: Alice, Betty, and Chase. Alice needs 3 bars, Betty needs 4 bars, and Chase needs 5 bars. How many ways are there to distribute the 12 bars to satisfy their requirements?	27,720	12%
Two subsets of the set S = {a, b, c, d, e} are to be chosen so that their union is S and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?	40	12%
There are 6 experienced applicants and 7 inexperienced applicants applying for a job. Out of the experienced applicants, 2 managers are selected. Out of all of the other applicants who aren’t selected for a manager (both experienced and inexperienced), 4 other employees are selected. How many ways are there to do this?	4950	12%
In a shooting match, eight clay targets are arranged in two hanging columns of three targets each and one column of two targets. A marksman is to break all the targets according to the following rules: 1) The marksman first chooses a column from which a target is to be broken. 2) The marksman must then break the lowest remaining target in the chosen column. If the rules are followed, in how many different orders can the eight targets be broken?	560	12%
Robert has 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has an engraving of one face on one side, but not on the other. He wants to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible distinguishable arrangements of the 8 coins.	630	12%
The number of subsets of a set of size n is	2^n	6%
How many ways are there to place 4 balls into a 4 × 6 grid such that no column or row has more than one ball in it? (Rotations and reflections are considered distinct.)	360	6%
Using the letters A, M, O, S, and U, we can form five-letter ”words”. If these ”words” are arranged in alphabetical order, then the ”word” USAMO occupies position	115	0%