Answer:
No, the note papers will not fit the gift box.
Step-by-step explanation:
Given that:
Volume of the gift box = 64
Length, width and height of the box all are equal to inches.
Dimensions of note papers = 6 inch by 6 inch
To determine:
Whether the note papers will fit the bottom of the box?
Solution:
Here, we need to find the dimensions of the gift box first.
If the dimensions of gift box are greater than or equal to the dimensions of the note papers, only then the papers will fit into the box.
As per the given question statement, the gift box is in the form of a cube.
Formula for volume of a cube is given as:
Side is given equal to inches.
Dimensions of the box are lesser than that of the note papers.
Therefore, <em>the note papers will not fit into the gift box</em>.
The recurring decimal number 9.2424... expressed in mixed number is
In the given decimal number, 2 is the digit at the tenth place and 4 is the digit at the hundredth place.
The fraction part in the simplest form is
The whole number part is 9.
Therefore, the number 9.2424... as a mixed number in the simplest form is
Answer:
The number of ways to deal each hand of poker is
1) 10200 possibilities
2) 5108 possibilities
3) 40 possibilities
4) 624 possibilities
5) 123552 possibilities
6) 732160 possibilities
7) 308880 possibilities
8) 267696 possibilities
Step-by-step explanation:
Straigth:
The Straight can start from 10 different positions: from an A, from a 2, 3, 4, 5, 6, 7, 8, 9 or from a 10 (if it starts from a 10, it ends in an A).
Given one starting position, we have 4 posibilities depending on the suit for each number, but we need to substract the 4 possible straights with the same suit. Hence, for each starting position there are 4⁵ - 4 possibilities. This means that we have 10 * (4⁵-4) = 10200 possibilities for a straight.
Flush:
We have 4 suits; each suit has 13 cards, so for each suit we have as many flushes as combinations of 5 cards from their group of 13. This is equivalent to the total number of ways to select 5 elements from a set of 13, in other words, the combinatorial number of 13 with 5 . However we need to remove any possible for a straight in a flush, thus, for each suit, we need to remove 10 possibilities (the 10 possible starting positions for a straight flush). Multiplying for the 4 suits this gives us
possibilities for a flush.
Straight Flush:
We have 4 suits and 10 possible ways for each suit to start a straight flush. The suit and the starting position determines the straight flush (for example, the straight flush starting in 3 of hearts is 3 of hearts, 4 of hearts, 5 of hearts, 6 of hearts and 7 of hearts. This gives us 4*10 = 40 possibilities for a straight flush.
4 of a kind:
We can identify a 4 of a kind with the number/letter that is 4 times and the remaining card. We have 13 ways to pick the number/letter, and 52-4 = 48 possibilities for the remaining card. That gives us 48*13 = 624 possibilities for a 4 of a kind.
Two distinct matching pairs:
We need to pick the pair of numbers that is repeated, so we are picking 2 numbers from 13 possible, in other words, possibilities. For each number, we pick 2 suits, we have
possibilities to pick suits for each number. Last, we pick the remaining card, that can be anything but the 8 cards of those numbers. In short, we have 78*6*6*(52-8) = 123552 possibilities.
Exactly one matching pair:
We choose the number that is matching from 13 possibilities, then we choose the 2 suits those numbers will have, from which we have possibilities. Then we choose the 3 remaining numbers from the 12 that are left (
) , and for each of those numbers we pick 1 of the 4 suits available. As a result, we have
possibilities
At least one card from each suit (no mathcing pairs):
Pick the suit that appears twice (we have 4 options, 1 for each suit). We pick 2 numbers for that suit of 13 possible ( possibilities ), then we pick 1 number from the 11 remaining for the second suit, 1 number of the 10 remaining for the third suit and 1 number from the 9 remaining for the last suit. That gives us 4*78*11*10*9 = 308880 possibilities.
Three cards of one suit, and 2 of another suit:
We pick the suit that appears 3 times (4 possibilities), the one that appears twice (3 remaining possibilities). Foe the first suit we need 3 numbers from 13, and from the second one 2 numbers from 13 (It doesnt specify about matching here). This gives us
possibilities.