Question

In how many ways a bag, consisting of 5 pens and 6 pencils can be filled from a stock having 8 pens and 10 pencils?

Answer 1

Answer:

9

Step-by-step explanation:

because we get 10 pencil in that 8 pens

Answer 2

Answer:  The required number of ways is 11760.

Step-by-step explanation:  We are given to find the number of ways in which a bag consisting of 5 pens and 6 pencils can be filled from a stock having 8 pens and 10 pencils.

Since the arrangements of the pens and pencils does not matter, so this is a problem of combination.

We have

The number of ways in which 5 pens can be selected from 8 pens is given by

$^8C_5=\dfrac{8!}{5!(8-5)!}=\dfrac{8\times7\times6\times5!}{5!\times3\times2\times1}=56$

and

the number of ways in which 6 pencils can be selected from 10 pencils is given by

$^{10}C_6=\dfrac{10!}{6!(10-6)!}=\dfrac{10\times9\times8\times7\times6!}{6!\times4\times3\times2\times1}=210.$

Therefore, the number of ways in which a bag consisting of 5 pens and 6 pencils can be filled from a stock having 8 pens and 10 pencils is given by

$n=^8C_5\times^{10}C_6=56\times210=11760.$

Thus, the required number of ways is 11760.