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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?

2 Answers

1 vote

The answer would be A) 210.

Marco is putting some sweaters into storage. He has 10 sweaters and can fit 6 sweaters-example-1
User Weihui Guo
by
8.6k points
3 votes

Answer:

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

User Bernardo Marques
by
8.5k points