Question

$\huge\tt\red{Ouestion:-}$

Two numbers are chosen from 1, 3, 5, 7,… 147, 149 and 151 and multiplied together in all possible ways. The number of ways which will give us the product a multiple of 5, is

Options:

(a) 75

(b) 1030

(c) 95

(d) 1020

(Give Full Answer with Explanation )​

Answer 1

Answer:

$(b)1030$

(b)1030

Answer 2

$\blue{\Large{\boxed{\tt{\purple{Explanation:- }}}}}$

Numbers which are multiple of 5 are

$\implies$ 5, 15, 25,.,145

a = 5, d = 10, n = ? $\small\tt{a^n = 145}$

$\implies$145 = 5 + (n − 1)10

$\implies$n=15

total number of terms in the given sequence is m ,then

$\implies$ 151 = 1 + (m − 1)

$\implies$ m = 76

So, the number of ways in which product is a multiple of 5=(both two numbers from 5, 15 , 25 ,..,145) or (one number from 5, 15, 25 ,..145 and one from remaining)

$\implies$$\tt{\frac{15 \times 14}{2} + 15 \times 61}$

$\implies$$\tt{105+915}$

$\implies$ $\tt{1020}$

$\underline\red{\underline{\sf{\maltese\: Answer\::-}}}$(d) 1020.

Hope it helps :)