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Q.
Two distinct numbers are chosen from $1,3,5,7........151,153,155$ and multiplied. The probability that the product is a multiple of $5$ is
NTA AbhyasNTA Abhyas 2020Probability
Solution:
Given numbers $1,3,5........,153,155$
$T_{n}=a+\left(n - 1\right)d\Rightarrow 155=1+\left(n - 1\right)2\Rightarrow n=78$
Total number of ways $=^{78}C_{2}=3003$
The numbers which are multiple of $5$ are $5,15,25,....,155$
$155=5+\left(n - 1\right)10\Rightarrow n=16$
The number of ways in which product is a multiple of $5=$ (Both two numbers from $5,15,25,......,155$ ) or (one number from $5,15,25,......,145$ and one number from the remaining numbers).
$=^{16}C_{2}+^{16}C_{1}\times ^{78 - 16}C_{1}$
$=\frac{816 \times 15}{2}+16 \times 62$
$=120+992=1112$