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Alisiya [41]
3 years ago
11

Four different sets of objects contain 2,5,6 and 7 objects respectively how many unique combinations can be formed by picking on

e object from each set
Mathematics
1 answer:
dusya [7]3 years ago
4 0

Answer:

420 unique combinations.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

One object from each set:

2 from one set, 5, 6 and 7 by others. Sets are independent, so, by the fundamental counting principle:

2*5*6*7 = 10*42 = 420

420 unique combinations.

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Simplify the following surds :<br><br> 1) 2√21 × √27 ÷ √343<br> 2) 7√5 × √125 ÷ 2√27
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Answer:

1) \frac{18}{7}

2) \frac{175\sqrt{3}}{18}

Step-by-step explanation:

* Lets explain how to simplify a square root

1)

∵ 2\sqrt{21} × \sqrt{27} ÷ \sqrt{343}

∵ \sqrt{21}=\sqrt{3} × \sqrt{7}

∴ 2\sqrt{21} = 2\sqrt{3} × \sqrt{7}

∵ \sqrt{27} = \sqrt{3} × \sqrt{3} × \sqrt{3}

∵ \sqrt{3} × \sqrt{3} = 3

∴ \sqrt{27} = 3\sqrt{3}

∴ 2\sqrt{21} × \sqrt{27} =

  2\sqrt{3} × \sqrt{7} × 3\sqrt{3}

∵ \sqrt{3} × \sqrt{3} = 3

∵ 2 × 3 × 3 = 18

∴ 2\sqrt{21} × \sqrt{27} = 18\sqrt{7}

∵ \sqrt{343} = \sqrt{7} × \sqrt{7} × \sqrt{7}

∵ \sqrt{7} × \sqrt{7} = 7

∴ \sqrt{343} = 7\sqrt{7}

∵ 2\sqrt{21} × \sqrt{27} ÷ \sqrt{343} =

  18\sqrt{7} ÷ 7\sqrt{7}

∵ \sqrt{7} ÷ \sqrt{7} = 1

∴ 2\sqrt{21} × \sqrt{27} ÷ \sqrt{343} =

  \frac{18}{7}

2)

∵ 7\sqrt{5} × \sqrt{125} ÷ 2\sqrt{27}  

∵ \sqrt{125} = \sqrt{5} × \sqrt{5} × \sqrt{5}

∵ \sqrt{5} × \sqrt{5} = 5

∴ \sqrt{125} = 5\sqrt{5}

∴ 7\sqrt{5} × \sqrt{125} =

  7\sqrt{5} × 5\sqrt{5}

∵ \sqrt{5} × \sqrt{5} = 5

∴ 7\sqrt{5} × \sqrt{125} = 7 × 5 × 5 = 175

∵ 2\sqrt{27} = 2\sqrt{3} × \sqrt{3} × \sqrt{3}

∵ \sqrt{3} × \sqrt{3} = 3

∴ 2\sqrt{27} = 6\sqrt{3}

∴ 7\sqrt{5} × \sqrt{125} ÷ 2\sqrt{27} =

  175 ÷ 6\sqrt{3} = \frac{175}{6\sqrt{3}}

∵ \frac{175}{6\sqrt{3}} not in the simplest form because

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∴ Multiply up and down by \sqrt{3}

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∴  \frac{175}{6\sqrt{3}} = \frac{175\sqrt{3}}{18}

∴ 7\sqrt{5} × \sqrt{125} ÷ 2\sqrt{27} =

  \frac{175\sqrt{3}}{18}

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