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Sav [38]
3 years ago
5

Meredith's goal is to read one library book each week. On the first night, she read 14 pages more than of the pages in the book.

If the book has 280 pages, how many pages did she
read the first night?
A 54
B
42
С
38
D
26
Mathematics
1 answer:
Murljashka [212]3 years ago
8 0

Answer: A : 54

Step-by-step explanation:

1/7 of 280+14

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Answer:

Step-by-step explanation:

As there are total 52 cards in a deck and we have to draw a set of 5 cards, we can use the formula of combination to find the total number of possible ways of drawing 5 cards.

Number of ways to draw 5 cards = N_T

N_T\;=\;({}^NC_k)\\\\N_T\;=\;({}^{52}C_5)\\\\N_T\;=\;2,598,960

(a) Assuming the cards are drawn in order (would not affect the probability). The of getting Ace, 2, 3, 4 and 5 can be obtained by multiplying the probability of getting cards below 6 (20/52) with the probability of getting 5 different cards (4 choices for each card).

P(a)\;=\;\frac{20}{52}*\frac{4}{52}*\frac{4}{51}*\frac{4}{50}*\frac{4}{49}*\frac{4}{48}\\\\P(a)\;=\; 1.3133*10^{-6}

(b) For a straight we require our set to be in a sequence. The choices for lowest value card to produce a sequence are ace, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Hence, the number of ways are ({}^{10}C_1).

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N_S\;=\;({}^{4}C_1)*({}^{4}C_1)^5\;=\;10240

Thus, the probability of getting a straight hand is:

P(b)\;=\;\frac{N_S}{N_T}\\\\P(b)\;=\;\frac{10240}{2598960}\\\\P(b)\;=\; 0.0039

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