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In the given problem, apply your knowledge in algebraic expression and basic mathematics especially in solving word problem about combinatorics.

Problem

A box contains 8 red balls, 7 blue balls, and 6 orange balls. In how many ways can 6 balls be chosen if there should be 2 balls each color?

Given

8 red balls

7 blue balls

6 orange balls

Solution

Use the formula for combination, nCr = n!/r!(n-r)!

If the restriction is 2 balls each color

→ nCr = nCr (red) × nCr (blue) × nCr (orange)

nCr = 8C2 × 7C2 × 6C2

nCr = 8!/2!(8-2)! × 7!/2!(7-2)! × 6!/2!(6-2)!

nCr = 28 × 21 × 15

nCr = 8 820

Answer

8 820 ways

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