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 : [tex]^nC_r =\frac{n!}{r!(n-r)!}[/tex]
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
[tex]^{10}C_6 =\frac{10!}{6!(10-6)!}[/tex]
[tex]^{10}C_6 =\frac{10!}{6!(4)!}[/tex]
[tex]^{10}C_6 =\frac{10 \times 9 \times 8 \times 7 \times 6!}{6!(4\times 3 \times 2 \times 1)}[/tex]
[tex]^{10}C_6 =\frac{10 \times 9 \times 8 \times 7}{4\times 3 \times 2 \times 1}[/tex]
[tex]^{10}C_6 =210[/tex]
Thus No. of possible groups of 6 sweaters is 210
