Question

Marco is putting some sweaters into storage. He has 10 sweaters and can fit 6 sweaters into a box. How many different groups of 6 sweaters can Marco pack into a box?

Answer 1

The answer would be A) 210.

Answer 2

210

Explanation:

Given : Marco has 10 sweaters and can fit 6 sweaters into a box.

To Find: How many different groups of 6 sweaters can Marco pack into a box?

Solution:

Since we are not given any sequence .

So, we will use combination over here.

Formula :
`^nC_r =(n!)/(r!(n-r)!)`

Since we are given that he has 10 sweaters and 6 can fit into a box .

So, n = 10

r = 6

Substitute the values in the formula

`^(10)C_6 =(10!)/(6!(10-6)!)`

`^(10)C_6 =(10!)/(6!(4)!)`

`^(10)C_6 =(10 * 9 * 8 * 7 * 6!)/(6!(4* 3 * 2 * 1))`

`^(10)C_6 =(10 * 9 * 8 * 7)/(4* 3 * 2 * 1)`

`^(10)C_6 =210`

Thus No. of possible groups of 6 sweaters is 210