Aptitude Training - PERMUTATIONS AND COMBINATIONS1
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The document details the concepts of permutations and combinations, illustrating how to calculate selections and arrangements. It presents various problems, including finding the number of persons in a party based on handshakes, inviting friends, counting diagonals in an octagon, rectangles in a chessboard, and forming a team with specific gender requirements. Answers and calculations for each problem are provided, highlighting the application of these mathematical principles.
Aptitude Training - PERMUTATIONS AND COMBINATIONS1
- 2. Basics : Permutation – arrangement Combination – selection • Out of n different things, if some or all the things are selected at a time, then each of these selections is called a Combination • Out of n different things, if r things are selected at a time, then the number of selections is given by = • and = • + + + + ….. • The number of ways in which we can select is given by .
- 3. 1. In a party, each person has to give a handshake to the other person only once. If the total number of handshakes exchanged in the party is 435, then find the number of persons in the party? 2. In how many ways can u invite at least one of your 8 friends to a party? 3. How many diagonals are there in an octagon? 4. How many rectangles are there in a chessboard? 5. Out of 5 boys and 4 girls, a team of 4 men can be selected. In how many ways can u select the team, such that there is at least one girl in the team? Combination :
- 4. In a party, each person has to give a handshake to the other person only once. If the total number of handshakes exchanged in the party is 435, then find the number of persons in the party? Ans : Handshake ( selecting 2 hands at a time) = = 435 ( ) = 435 n = 30 Number of persons = 30 1. number of persons in the party = 30
- 5. In how many ways can u invite atleast one of your 8 friends to a party?2. + + ….. We know that + + + + ….. X=1 , n =8
- 6. How many diagonals are there in an octagon?3. Ans : To draw a polygon with n sides, we require n non-collinear points. The total number of line segments that can be drawn using n non-collinear points is given by Number of diagonals = - n ( n = number of sides ) In the given question, N = 8 => Number of diagonals = - 8 Number of diagonals = 20
- 7. How many rectangles are there in a chessboard?4. Ans : If a set of m parallel lines intersect with another set of n parallel lines then the total number of parallelograms formed are Total number of parallelograms formed in chess board = = 1296 Total number of squares in a chessboard = 204 Total number of rectangles = 1296 – 204 = 1092. Total number of rectangles = 1092
- 8. Out of 5 boys and 4 girls, a team of 4 should be selected. In how many ways can u select the team, such that there is atleast one girl in the team? 5. Ans : 1G, 3B ; 2G, 2B ; 3G, 1B ; 4G or ( any 4 – 4B ) Number of ways = + + + = 121 OR Number of ways = = 121 Number of ways = 121
- 9. Subscribe to : Problems for practice are given in the description of the video.