Question

How many different values we can get by multiplying two different numbers from the set {9, 25, 27, 81, 125, 243, 625, 729, 3125}?

Answer 1

Given: the given set is {9, 25, 27, 81, 125, 243, 625, 729, 3125}

To find: how many different values we can get by multiplying two different numbers from the above set ?

Solution:

1. We multiply 9 with the rest numbers. So there are 8 products.
2. Now we exclude 9 from the list and we multiply 25 with the rest numbers. So there are 7 products.
3. In this way, excluding the numbers 25, 27, ..., 625, we get 6, 5, ..., 1 products respectively.

Thus total number of products is

= 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36

Answer: Thus we get 36 different values when we multiplying two different numbers from the given set.

ALTERNATIVE METHOD:

• Given, 9 numbers and to find product of two numbers: we use combination:
• ⁹C₂ = 36
• This is the number of different values.