1/30/2024 0 Comments 16 permute 3![]() The digits in the PIN from left to right are in decreasing order. There is a numeric lock which has a 3-digit PIN. How many such arrangements are possible? (UPSC 2022)Ģ0. The letters A, B, C, D and E are arranged in such a way that there are exactly two letters between A and E. In how many ways can the mice be placed into three groups?.ġ9. 20 mice were placed in two experimental groups and two control group, with all groups equally large. What is the number of different sums of money the person can form?ġ8. A person has 4 coins if different denominations. Using all the letters of the word GIFT how many distinct words can be formed?ġ7. How many motor vehicle registration number plates can be formed with digits 1,2,3,4,5 (no digits being repeated) if it is given that registration number can have 1 to 5 digits?ġ6. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?ġ5. 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?ġ4. Find the number of permutations of the letters of the word ALLAHABAD.ġ3. In how many ways can the letters of the word 'LEADER' be arranged?ġ2. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. How many numbers are there in all from 6000 to 6999 (both 60 included) having at least one of their digits repeated?ġ0. ![]() In how many ways can the assignment be done? (UPSC 2015)ĩ. Task-2 must be assigned to either person-3 or person-4. Task-l cannot be assigned to either person-l or person-2. What was the number of pairs of brown socks in the original order? (UPSC 2015)Ĩ. While preparing the bill, the bill clerk interchanged the number of black and brown pairs by mistake which increased the bill by 100%. The price of a black pair was thrice that of a brown pair. A person ordered 5 pairs of black socks and some pairs of brown socks. In how many different ways can six players be arranged in a line such that two of them, Asim and Raheem are never together?ħ. What is the maximum number of such different groups?Ħ. Groups each containing 3 boys are to be formed out of 5 boys A,B,C,D and E such that no one group contains both C and D together. In how many different ways can this be done?ĥ. Six identical balls are to be placed in these smaller squares such that each of the three rows gets at least one ball (one ball in one square only). A square is divided into 9 identical smaller squares. How many three-digit numbers can be generated from 1, 2, 3, 4, 5, 6, 7, 8, 9, such that the digits are in ascending order?Ĥ. There are 7 candidates for 3 seats, in how many ways the post be filled?ģ. In how many different ways can five friends sit for a photograph of five chairs in a row?Ģ. making people sit, putting letters in envelopes, finishing order in horse race, etc.)ġ. Putting distinct objects/people in distinct places, e.g.Selection of batting order of a cricket team of 11 from 16 members.Making words and numbers from a set of available letters and digits respectively.Some typical situations where ordered selection/ permutations are used: NPr = number of permutations (arrangements) of n things taken r at a time. In other words permutations can also be referred to as an ORDERED SELECTION. Hence please understand here that the order in which the r things are arranged has critical importance in the counting of permutations. Permutations can be defined as the number of ways in which r things at a time can be SELECTED & ARRANGED at a time from amongst n things. In other words any selection in which the order of selection holds no importance is counted by using combinations. Selection of a set of objects (like letters, hats, points pants, shirts, etc) from amongst another set available for selection.Selection of a cricket team of 11 from 16 members) Selection of people for a team, a party, a job, an office etc.Some typical situations where selection/combination is used: Where n ≥ r (n is greater than or equal to r). NCr = Number of combinations (selections) of n things taken r at a time. Please understand here that the order in which the r things are selected has no importance in the counting of combinations. Factorials of only Natural numbers are defined.Ĭombinations can be defined as the** number of ways in which r things at a time can be SELECTED from amongst n things** available for selection.n! = n(n – 1) (n – 2) …3.2.1 = Product of n consecutive integers starting from 1.
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