PERMUTATION A 5-item MCQ Guiliver Eduard L. Van Zandt Ramon Magsaysay (Cubao) High School

Directions Read the questions carefully. Analyze, solve, and click on the colored circle beside the number which corresponds to your answer. Good luck!

A group of 5 friends are planning to pose for a picture in a linear formation. How many distinct photographs can be taken?

Congratulations! You are CORRECT. Complete Solution: For linear permutation (P linear ), the formula is P linear = n!, where n is the number of objects to be arranged in a linear formation. Since there are 5 persons to be arranged in linear formation, then P = 5! = 5x4x3x2x1 = 120

Among the 5, two insisted to pose beside each other. In how many ways can this be done?

Congratulations! You are CORRECT. Complete Solution: This problem is still on linear permutation. But there is an additional condition that 2 of them must always be beside each other. This is having a linear permutation within a linear permutation. So, instead of 5, consider only 4 because 2 of them must be together, that is 4!. Next, take the permutation of the 2 persons who insist to be together, that is 2!. Finally, the final answer is the product of the two results, that is 4! X 2! = (4x3x2x1) x (2x1) = 48

Then suddenly these two refuse to pose beside each other. How many arrangements are possible considering this condition?

Congratulations! You are CORRECT. Complete Solution: In this question, we want to find the number of permutations where 2 of them must not be next to each other. Take note that in no. 1, we were able to conclude that there are 120 permutations regardless whether the 2 are beside each other or not). In no. 2, we were able to say that there are 48 permutations where two of them are beside each other. Considering this two solutions, we can get the no. of permutations where these 2 are not beside each other by getting the difference of the two results earlier, that is P(not together) = P(5 in linear) – P(2 must be together) =120 – 48 =72

Then they went to a coffee shop to have some snacks. The tables there are all round. In how many ways can they be seated?

Congratulations! You are CORRECT. Complete Solution: For circular permutation (P linear ), the formula is P linear = (n-1)!, where n is the number of objects to be arranged in a circular formation. Since there are 5 persons to be arranged in circular formation, then P = (5-1)! = 4x3x2x1 = 24

If two among the 5 insist of sitting next to each other, then how many ways can they be seated around the table?

Congratulations! You are CORRECT. Complete Solution: This problem is again on circular permutation. But there is an additional condition that 2 of them must always be beside each other. This is having a linear permutation within a circular permutation. So, instead of 5, consider only 4 persons to be arranged in circular because 2 of them must be together, that is (4-1)!. Next, take the permutation of the 2 persons who insist to be together, this is in linear, that is 2!. Finally, the final answer is the product of the two results, that is (4-1)! X 2! = (3x2x1) x (2x1) = 12

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