Question
# In how many ways 5 red and 4 white balls be drawn from a bag Containing 10 red and 8 white balls? A) ${}^8C_{5} \times {}^{10}C_{4}$B) ${}^{10}C_{5} \times {}^8C_{4}$C) ${}^{18}C_{9}$D) ${}^{18}C_{5} \times {}^{18}C_{4}$
Hint: In this question it is given that We have to find in how many ways 5 red and 4 white balls can be drawn from a bag Containing 10 red and 8 white balls. So to find the solution we need to know that if we have given n number of quantities then one can select r number of quantity in ${}^nC_{r}$ ways.
A Bag contains 10 red balls and 8 white balls, so from the 10 red balls 5 red balls can be selected in ${}^{10}C_{5}$ ways and similarly we can say that from 8 white balls 4 balls can be selected in ${}^{8}C_{4}$ ways.
So by the fundamental principle of multiplication we can say that, 5 red and 4 white balls can be selected in ${}^{10}C_{5} \times {}^8C_{4}$ ways.
Note: Fundamental principle of multiplication is the rule of multiplication which states that, if there are a ways of doing something and b ways of doing another thing, then there are a$\times$ b ways of performing both actions.