permutations

Question

The number of ways in which 5 boys and 3 girls can be arranged in a row so that all girls sit together is

RankGuru · Accepted Answer

1. **Grouping Strategy**: Treat the 3 girls as a single 'block' or unit.
2. **Arrange the Units**: 
   - We now have 5 boys + 1 block of girls = 6 units.
   - Arrangement of 6 distinct units = $6! = 720$.
3. **Internals of Block**: The 3 girls within the block can be arranged among themselves in $3!$ ways.
   - $3! = 6$.
4. **Total Calculation**:
   - Total Ways $= 6! 	imes 3!$
   - $= 720 	imes 6 = 4,320$.
5. **Result**: 4,320 ways.

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