How many ways can you deal a hand of 13 playing cards that contain four spades, seven diamonds, and two hearts? Explain

How many five-digit numbers can be formed from the set if nine numbers {0,1,2,3,4,5,6,7,8} if no number is repeated and no number starts with zero, and
a) there are no other restrictions?
b) the result must be an odd number?

Use pascals triangle to show all of the paths that the checker piece can take to reach the bottom square marked with an x, without going through the two blacked-out squares. The checker piece can only move diagonally forwards by one sqaure at a time, in this case, using white squares only. The checkerboard is uploaded.

The values of a computer in the years after its purchase date are listed in the table that has been uploaded. Given that the equation of the regression line between value and year is y=-207.14x+1507.14 with an R^2 value of 0.9622, how reliable do you think the regression equation is at predicting the future value of a computer in five years’ time?

Identify what if any bias is found in each of the following sampling scenarios. Explain. There are household bias, sampling bias, non-response bias, and response bias.
A) selecting some residents of a building to participate in a survey of recycling options based on the last digit of their phone number.
B) polling members of a business association to gauge public reaction to a proposed new business tax.

How many ways can you deal a hand of 13 playing cards that contain four spades, seven diamonds, and two hearts? Assume that the deck is a standard 52-card deck. Leave your answer in factorial form.

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