Question

Eight chairs are numbered 1 to 8. Two women and 3 men wish to occupy one chair each. First the women choose the chairs from amongst the chairs 1 to 4 and then men select from the remaining chairs. Find the total number of possible arrangements.

Answer 1

We have 2 women and 3 men

First women choose the chairs amongst the chairs 1 to 4

i.e. Total number of chairs = 4

So, the number of arrangements = ⁴P₂ ways

Now 3 men choose from the remaining 6 chairs

So, the number of arrangements = ⁶P₃ ways

∴ Total number of arrangements = ⁴P₂ × ⁶P₃

= ${\displaystyle \frac{4!}{(4-2)!}\times \frac{6!}{(6-3)!}}$

= ${\displaystyle \frac{4!}{2!}\times \frac{6!}{3!}}$

= ${\displaystyle \frac{4\cdot 3\cdot 2!}{2!}\times \frac{6\cdot 5\cdot 4\cdot 3!}{3!}}$

= 12 × 120

= 1440

Hence, the total number of possible arrangements are 1440.