Quant - Permutation & Combinations Flashcards
Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?
https://gmatclub.com/forum/pat-will-walk-from-intersection-x-to-intersection-y-along-a-route-that-68374.html
In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.
So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U’s and 2 identical R’s is 5!/3!2!=10.
Alex and Sam are playing a game of dice. Sam, being the evil one, loaded the dice in such a way that the probability of getting any number n is n times the probability of showing up of 1 when the dice is rolled. The rules of the games are such that for every time an odd number shows up, Alex scores a point, otherwise the point goes to Sam. What is the probability of Alex scoring a point at any single roll?
Let the probability of getting 11 is 1x1x, so probability of getting 2,3,4,5,62,3,4,5,6 is 2x,3x,4x,5x,6x2x,3x,4x,5x,6x respectively.
As these are the only possibilities, their probability should add up to 1…..1x+2x+3x+4x+5x+6x=1…..1+2+3+4+5+6x=21x=1….x=211x+2x+3x+4x+5x+6x=1…..1+2+3+4+5+6x=21x=1….x=21
Probability of getting odd number = 1x+3x+5x…..1+3+5x=9/21=3/7
The map above shows the trails through a wilderness area. If travel is in the direction of the arrows, how many routes along the marked trails are possible from point A to point B ?
https://gmatclub.com/forum/the-map-above-shows-the-trails-through-a-wilderness-area-if-travel-is-305847.html
The cardinality of a finite set is the number of elements in the set. What is the cardinality of set A ?
(1) 2 is the cardinality of exactly 6 subsets of set A.
(2) Set A has a total of 16 subsets, including the empty set and set A itself.
https://gmatclub.com/forum/the-cardinality-of-a-finite-set-is-the-number-of-elements-in-the-set-305929.html
Ans = D
This is a P&C question masquerading as a Sets question. Perhaps that is why it seems confusing.
Cardinality = Number of elements in the set
So say set A has n elements. Then its cardinality is n.
We need to find the number of elements in set A.
(1) 2 is the cardinality of exactly 6 subsets of set A.
When, from set A, we make all subsets, exactly 6 subsets have 2 elements each. Think about it - if you have a set with n elements. How will you make subsets with exactly 2 elements? How many such distinct subsets can you make? In nC2 ways.
So we are given that nC2 = 6
Then n must be 4 because 4C2 = 6. For all greater values of n, nC2 will be greater.
Sufficient alone.
(2) Set A has a total of 16 subsets, including the empty set and set A itself.
From the n elements of set A, total how many subsets can you make? For each element, you can either select it or ignore it. So each element can he handled in 2 ways. IF w have n elements, we get 222*.. n times
We are given that 2^n = 16
n = 4
Sufficient alone.
Answer (D)
Take an example to help see it clearly. Say set A = {5, 7, 8, 9}
How many subsets can you make with exactly 2 elements? 4C2 = 6. They will include {5, 7}, {5, 8}, {5, 9}, {7, 8}, {7, 9} and {8, 9}
How many total subsets can you make? You can take the 5 or ignore. You can take the 7 or ignore etc. You have subsets ranging from {}, {5}, {7}, … till {5, 7, 8, 9}
The table above shows the number of residents in each of two age groups who support the use of each type of funding for a city initiative. What is the probability that a person randomly selected from among the 250 residents polled is younger than 40, or supports a type of funding that includes a tax, or both?
A. 1/5 B. 8/25 C. 12/25 D. 3/5 E. 4/5
https://gmatclub.com/forum/the-table-above-shows-the-number-of-residents-in-each-of-two-age-group-305918.html
D
