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5 pairs of footwears are to selected out of 4 pairs of shoes and 6 pairs of sandals. In how many ways this can be done if there should be at least 3 pairs of shoes?

5 pairs of footwears are to selected out of 4 pairs of shoes and 6 pairs of sandals. In how many ways this can be done if there should be at least 3 pairs of shoes? Correct Answer 66

GIVEN:

5 pairs of footwears are to selected out of 4 pairs of shoes and 6 pairs of sandals.

CONCEPT:

Basic concept of Permutation and combination.

Number of ways to select ‘a’ out of ‘b’ = bCa

CALCULATION:

There are 4 pairs of shoes and 6 pairs of sandals.

5 pairs of footwear is to selected such that there should be at least 3 pairs of shoes.

There are 2 possible cases:

3 pairs of shoes and 2 pairs of sandals + 4 pairs of shoes and 1 pairs of sandals

∴ Total number of ways = 4C3 × 6C2 + 4C4 × 6C1

⇒ 4 × 15 + 1 × 6

⇒ 66

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