One hundred tickets, numbered 1,2,3, ,100, are sold to 100 different people for a drawing. four different prizes are awarded, including a grand prize (a trip to tahiti).

There are four questions related to this: how many number of ways are there to award the prizes if:

a)      There are no restrictions?  If k unalike awards are there for n people and no person can get more than one prize then there are: This leads to 100 × 99 × 98 × 97 = 94109400100 × 99 × 98 × 97 = 94109400 ways in your case where n=100 k=4.

b)The person holding ticket 47 wins the grand prize? After handing out the grand prize there are k=3 different rewards left for n = 99 persons. Apply the same formula.  941094941094

c)  The person holding ticket 47 wins one of the prizes? 4 times case because there are 4 likelihoods when it comes to the rewards that can be won by person 47.  37643763764376 

d) The person holding ticket 47 does not win a prize? k=4 and n =99. Person 4747 is left out.  9034502490345024 

e) The person holding ticket 19 and 47 both wins prize? First gave out a prize to 47. There are 4 possibilities. Then give out a prize to 19. There are 3 likelihoods. Then the other prizes are gave out: k=2 and n=98. Lastly you come to 4 × 3 × 98 × 97 =1140724 × 3 × 98 × 97 = 114072 possibilities.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

quit

step-by-step explanation: