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lana66690 [7]
2 years ago
9

A shelf can be packed from end to end with 30 large books or 45 small books.

Mathematics
1 answer:
DerKrebs [107]2 years ago
4 0

Answer:

11

Step-by-step explanation:

since 30÷45 = 2/3 then

The space taken by a small book is equal to

the space taken by 2/3 a large book.

…………………………………………………

<u><em>Calculating the number of large book corresponding to 23 small books</em></u> :

= 23×(2÷3) + 3

= 18.333333333333 (large book)

Then ,Kevin can pack the shelf with (at most) : 30 - 19 = 11 more large books

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A deck of 52 cards contains 12 picture cards. If the 52 cards are distributed in a random manner among four players in such a wa
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Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = \frac{12!}{3! 3! 3! 3!}

Now,

The Total number of ways in which Remaining cards are distributed = \frac{40!}{10! 10! 10! 10!}

So,

Total number of ways of getting 3 picture card and remaining card = \frac{12!}{3! 3! 3! 3!}× \frac{40!}{10! 10! 10! 10!}

= \frac{12! 40!}{(3!)^{4} (10!)^{4}  }

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = \frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }

∴ The probability = \frac{\frac{12! 40!}{(3!)^{4} (10!)^{4}  }}{\frac{52!}{(13!)^{4} }}

                            = \frac{12! 40!}{(3!)^{4} (10!)^{4}  }×\frac{(13!)^{4} }{ 52! }

                           = \frac{12! 40!}{(3!)^{4} (10!)^{4}  }×\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }

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                           = 0.0324

∴ we get

The probability that each player will receive three picture cards = 0.0324

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