Thus, the following are the number of possible choices:ĥ2C18 × 35C2 (18 families having at most 2 children and 2 selected from other types of families) Program, 20 families are to be chosen for assistance, of which at least 18 families must have at most 2 children. However, according to the question, for the rural development It is given that out of 87 families, 52 families have at most 2 children so the other 35 families are of other types. Now, in how many ways can the choice be made?Īns. In the same way a rural development program, 20 families are to be chosen for assistance, of which at least 18 families must have at most 2 children. 5) In a small village, there are 87 families, of which 52 families have almost 2 children. Hence, the committee can be chosen in 7C3 × 5C2 = 350 ways. 4) In how many ways can a committee consisting of 3 men and 2 women choose from 7 men and 5 women? (A) 45 (B) 350 (C) 4200 (D) 230Īccording to the combination formula, out of 7 men, 3 men can be chosen in 7C3 ways, and out of 5 women, 2 women can be chosen in 5C2 ways. Hence, the total number of possible choices is 35 + 6 = 41. In how many ways can he choose the three books to be borrowed?īoy borrows Mathematics Part II, then he borrows Mathematics Part I also.īoy does not borrow Mathematics Part II, then the number of possible choices is 7C3 = 35. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. Therefore, according to the combination formula, the required number of ways isĦC4 × 7C6 + 6C5 × 7C5 + 6C6 × 7C4 = 105 + 126 + 35 = 266 3) A boy has 3 library tickets and 8 books of his interest in the library. If there are 6 questions in Part A and 7 in Part B, in how many ways can the student choose 10 questions? 2) A student has to answer 10 questions, choosing at least 4 from each of Parts A and B. Hence, according to the combination formula, In choosing a committee, the order doesn’t matter, so we need the combination without repetition formula. We already chose Mr Smith, so we need to choose another 3 from 8 people. Smith must be one of the people selected? How many ways can a committee of 4 be chosen from 9 people given that Mr. However, the combination formula determines the combination of r things taken from n at a time without repetition.Īs an example, if you have four types of paints (n = 4) in your hand and you can choose only three (r = 3), hence, the number of ways to choose the paints with repetition can be calculated as 4C3. Note: The above-mentioned formula can be used only when we select the objects from a set without repetition.
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