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densk [106]
3 years ago
13

A textbook search committee is considering

Mathematics
1 answer:
lora16 [44]3 years ago
3 0

Number of ways to select 3 books from 13 books for adoption is 286 .

<u>Step-by-step explanation:</u>

A Permutation is an ordered Combination. When the order does matter it is a Permutation. There are basically two types of permutation:

  • Repetition is Allowed: such as the lock above. It could be "333".
  • No Repetition: for example the first three people in a running race. You can't be first and second.

Formula is given by:

nC_r= \frac{n!}{r! (n-r)!} , where n is the number of things to choose from,  and we choose r of them,  no repetitions,  order matters. Here , n=13 , r=3.

⇒ 13C_3 = \frac{13!}{3!(13-3)!}

⇒ 13C_3 = \frac{13!}{3!(10)!}

⇒ 13C_3 = \frac{13(12)(11)10!}{3(2)(1)(10)!}

⇒ 13C_3 = 13(2)(11)

⇒ 13 C_3 = 286

∴ Number of ways to select 3 books from 13 books for adoption is 286 .

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Step-by-step explanation:

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convert mixed numbers to improper fractions: 3 1/4 / 2/3

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apply the fraction rule: a/b / c/d = a/b * d/c

= 13/4 * 3/2

multiply fractions: a/b * c/d = (a * c)/(b * d)

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multiply the numbers: 13 * 3 = 39

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multiply the numbers: 4 * 2 = 8

= 39/8

convert improper fractions to mixed numbers: 39/8 = 4 7/8

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