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) ${}^{18}C_{5} \times {}^{18}C_{4}$

Answer 1

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.
Complete step-by-step solution:
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.
So the correct option is option B.
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.