Question

How many different ways can 10 letters be posted in 5 post boxes?

Answer 1

Answer:

10 letters can be posted in 5 post boxes by 1260 ways.                                              

Step-by-step explanation:

Given that-

Numbers of letter = 10

Numbers of post boxes = 5

10 letters can be posted in 5 post boxes by = n$C_{r}$

                                                                         = $\dfrac{n!}{r1(n-r)!} }$

Where n = number of letters

r = number of post boxes

So, the different ways to post letters = 10$C_{5}$

                                                             = $\dfrac{n!}{r1(n-r)!} }$

                                                             = $\dfrac{10!}{5!(10-5)!}$

                                                             = $\dfrac{10!}{5! \times5!}$

  = $\dfrac{10 \times9 \times8 \times7 \times6 \times5!}{5! \times5!}$

  = $\dfrac{10 \times9 \times8 \times7 \times6 \times5 }{5 \times 4\times 3\times 2\times 1}$

= $\dfrac{151200}{120}$

= 1260

Hence, 10 letters can be posted in 5 post boxes by 1260 ways.