![]() We’ll have to divide our counting into 2 cases. (iii) In this case, we’ll remove A 2 from the group, and select any 4 from the remaining group of 9 people – in 9C 4 ways. Now, out of the remaining 8, we’ve to select 2 more. (ii) In this case, we must select A 1 and A 3. (vi) A 9 is selected if and only if a A 10 is selected (v) if A 5 is selected then A 7 must not be selected (iv) if A 6 is selected then A 4 must also be selected The number of ways will be 10C 7 = 120Įxample 2 Find the number of ways in which a team of 4 can be selected from a group of 10 people A 1, A 2, A 3, …, A 10 such that Solution This is a simple case of selection of 7 objects (questions) out of 10 distinct objects. In how many ways can the student make his selection? This lesson will cover a few examples relating to combinations.Įxample 1 A question paper consists of 10 questions of which a student needs to answer any 7. The hundreds place can now be filled by any of the remaining 4 digits. ![]() So, there are 5 ways of filling the tens place. The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). Q.10: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?Įxplanation: Since each desired number is divisible by 5, so we must have 5 at the unit place. Q.9: In how many ways can the letters of the word 'LEADER' be arranged?Įxplanation: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R. Latest Aptitude and Logical Reasoning Test – Download Now! More than 1000+ detailed question and answers Prepare for Quantitative Aptitude, Maths, Logical Reasoning 2023 The number of possible combinations of selectees is:Įxplanation: Total number of ways = 2C 1. Q.8: A selection is to be made for one post of principal and two posts of vice-principal amongst the six candidates called for the interview only two are eligible for the post of principal while they all are eligible for the post of vice-principal. ![]() Hence, the required number of straight lines = 11C 2 – 6C 2 – 5C 2 + 1 + 1 How many straight lines, including the first two, can be formed with these points?Įxplanation: We know that, the number of straight lines that can be formed by the 11 points in which 6 points are collinear except those that can be selected out of these 6 points are collinear. Q.7: Six points are marked on a straight line and five points are marked on another line which is parallel to the first line. SSC Exam Test and Preparation 2023 – Download Now! More than 1200+ detailed question and answers Prepare for SSC CGL, CHSL, SSC MTS, Junior Engineer 2023 Q.6: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is:Įxplanation: Number of words which can be formed = 5! – 1 = 120 – 1 = 119 How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?Įxplanation: The total number of stations = 20įrom 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 20P 2 ways. Q.5: There are 18 stations between Hyderabad and Bangalore. Permutation – Basic Concepts, Methods, Examples, Math Tricks to Solve (Part 2) (Quantitative Aptitude made Simpler) ![]() Using these letters the number of 8 letters words formed is 8P 8 = 8! Q.4: Using all the letters of the word 'THURSDAY', how many different words can be formed? The number of 4 digit numbers that can be formed using six digits is 6P 4 = 6 * 5 * 4 * 3 = 360 Q.3: How many 4 digit numbers can be formed using the digits (1, 3, 4, 5, 7, 9) when repetition of digits is not allowed? Permutation – Basic Concepts, Methods, Examples, Math Tricks to Solve (Part 1) (Quantitative Aptitude made Simpler) Number of ways such that two ladies are always included in the committee = 6C 3 = (6 * 5 * 4) / 6 = 20 In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?Įxplanation: There are three ladies and five gentlemen and a committee of 5 members to be formed. Q.2: A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. To find how many 4 letter word we can find from that = 10*9*8*7 = 5040 Questions and Solved Examples on Permutation and Combination Q.1: How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?Įxplanation: The Word LOGARITHMS contain 10 letters. Number of diagonals in a geometric figure of n sides = nC 2-n. ![]()
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