{"id":3740,"date":"2024-03-05T15:55:06","date_gmt":"2024-03-05T15:55:06","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=3740"},"modified":"2024-03-05T15:55:06","modified_gmt":"2024-03-05T15:55:06","slug":"the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-queue-given-that-the-2-girls-have-to-be-next-to-each-other-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-ways-in-which-3-boys-and-2-girls-can-be-arranged-in-a-queue-given-that-the-2-girls-have-to-be-next-to-each-other-is\/","title":{"rendered":"The number of ways in which 3 boys and 2 girls can be arranged in a queue, given that the 2 girls have to be next to each other, is"},"content":{"rendered":"

[amp_mcq option1=”12″ option2=”24″ option3=”48″ option4=”120″ correct=”option3″]<\/p>\n

The correct answer is (c) 48.<\/p>\n

We can think of the 5 people as 2 groups: the 2 girls and the 3 boys. The 2 girls can be arranged in 2! ways, and the 3 boys can be arranged in 3! ways. So the total number of ways to arrange the 5 people is $2!3! = 48$.<\/p>\n

Here is another way to think about it. Imagine that the 2 girls are always together, like a single unit. Then we have 4 people to arrange, and there are $4!$ ways to do this. But the 2 girls can be arranged within their group in 2! ways, so we have to multiply $4!$ by 2! to get the total number of arrangements: $4!2! = 48$.<\/p>\n

Option (a) is incorrect because it is the number of ways to arrange 5 people without any restrictions. Option (b) is incorrect because it is the number of ways to arrange 3 boys and 2 girls if the girls must be in different positions. Option (d) is incorrect because it is the number of ways to arrange 3 boys and 2 girls if the girls must be in the same position.<\/p>\n","protected":false},"excerpt":{"rendered":"

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