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

There are 210 different groups. Hope it help!

Answer 2

Answer:

210

Step-by-step 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 : $^nC_r =\frac{n!}{r!(n-r)!}$

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

 $^{10}C_6 =\frac{10!}{6!(10-6)!}$

 $^{10}C_6 =\frac{10!}{6!(4)!}$

 $^{10}C_6 =\frac{10 \times 9 \times 8 \times 7 \times 6!}{6!(4\times 3 \times 2 \times 1)}$

$^{10}C_6 =\frac{10 \times 9 \times 8 \times 7}{4\times 3 \times 2 \times 1}$

$^{10}C_6 =210$

Thus No. of possible groups of 6 sweaters is 210