Question

An Earth scientist is testing how various soil mixtures affect plant growth. She begins with 10 soil types. For each mixture, she combines equal amounts of 2 soil types. How many soil mixtures must the scientist create in order to test all possible combinations of the 10 soil types?a. 20b. 45c. 55d. 90

Answer 1

Answer:

b

Explanation:

The correct answer would be 45.

Assuming that the 10 soils are each represented by A, B, C, D, E, F, G, H, I, J.

A can combine with 9 others as: AB AC AD AE A F AG AH AI AJ

B can combine as: BC BD BE BF BG BH BI BJ

C as: CD CE CF CG CH CI CJ

D as: DE DF DG DH DI DJ

E as: EF EG EH EI EJ

F as: FG FH FI FJ

G as: GH GI GJ

H as: HI HJ

I as: IJ

Adding all the combinations together = 45

In other words;

$^{10}C_2$ = $\frac{10!}{(2!(10 - 2)!)}$ = 45