A prize bag contains 1 hologram pencil, 7 blue-striped pencils, and 2 flowered pencils. If two pencils are randomly chosen from the prize bag, how many different color combinations are possible?

Question

Mathematics

Payton Huffman

8 November, 04:32

A prize bag contains 1 hologram pencil, 7 blue-striped pencils, and 2 flowered pencils. If two pencils are randomly chosen from the prize bag, how many different color combinations are possible?

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Answers (1)

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John Sandoval · Answer 1

45 different color combinations are possible if two pencils are randomly chosen from the prize bag.

Step-by-step explanation:

The bag contains 1 hologram pencil + 7 blue-striped pencils + 2 flowered pencils.

So, the prize bag contains 10 pencils in total.

Combination formula C (n, r) = n!/r! (n-r) !

where n = 10 pencils, Out of these 10 pencils, only 2 pencils are randomly chosen. So, r = 2.

The 10 pencils can be arranged in 10! (10*9*8*7*6*5*4*3*2*1) ways.

C (10,2) = 10! / (2!) (10-2) !

= 10! / (2!) (8!) = 10*9*8! / 2!*8!

= 10*9 / 2*1

= (5*9) = 45 different combinations.