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  • Two numbers are to be chosen from 1, 3, 5, 7,… 147, 149 and 151 and multiplied together in all possible ways. How many ways are possible to obtain a product that is a multiple of 5? <

Two numbers are to be chosen from 1, 3, 5, 7,… 147, 149 and 151 and multiplied together in all possible ways. How many ways are possible to obtain a product that is a multiple of 5?

 

Option: 1

1060


Option: 2

1020


Option: 3

2400


Option: 4

4800


Answers (1)

In the numbers 1, 3, 5, 7,…, 147, 149, 151, the numbers multiples of 5 are 5, 15, 25, 35, …, 145, which form an arithmetic sequence.
\begin{aligned} &T_n=a+(n-1) \times d\\ &145=5+(n-1) \times 10 \end{aligned}
n = 15
and if the total number of terms in the given sequence is m, then 
 151=1+(m-1) \times 2
m = 76
So, the number of ways in which a product is a multiple of 5 = (both two numbers from 5, 10, 15, 20, 25, 30, 35, … , 150) or (one number from 5, 10, 15, 20, 25, 30, 35, …, 150 and one from remaining numbers) 

\begin{aligned} & =15 C_2+15 C_1 \times(76-15) C_1 \\ & =105+15 \times 61 \\ & =1020 \end{aligned}

 

 

 

 

Posted by

Sumit Saini

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