Subjects combinatorics

Girls Boys Seating 015D4D

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1. **Problem statement:** We have two girls (Arta, Besa) and three boys (Dioni, Ermiri, Flamur) who want to sit in a row of five seats such that the girls sit next to each other and the boys also sit next to each other. 2. **Understanding the problem:** We want to count the number of ways to arrange these five people with the constraint that the two girls are together and the three boys are together. 3. **Approach:** Treat the group of girls as one block and the group of boys as another block. So, we have two blocks to arrange: G (girls block) and B (boys block). 4. **Number of ways to arrange the blocks:** There are 2 blocks, so they can be arranged in $2! = 2$ ways (GB or BG). 5. **Number of ways to arrange the girls inside their block:** The two girls can be arranged in $2! = 2$ ways. 6. **Number of ways to arrange the boys inside their block:** The three boys can be arranged in $3! = 6$ ways. 7. **Total number of arrangements:** Multiply the number of ways to arrange the blocks by the number of ways to arrange girls and boys inside their blocks: $$ 2! \times 2! \times 3! = 2 \times 2 \times 6 = 24 $$ **Final answer:** 24 ways. Therefore, the correct choice is b) 24.