Non Calculator and Calculator Mathematics Problems Questions Kindly solve all problems in the attached, you need to show all the steps for each problems Ma

Non Calculator and Calculator Mathematics Problems Questions Kindly solve all problems in the attached, you need to show all the steps for each problems Math Questions
Show all steps please.
1. P (8, 3)
2. C (7, 4)
Show all steps please.
1. Using the digits 0, 1, 2…, 9, how many 7-digit numbers can be formed if the first digits
cannot be a 0 or 9 and the last digit must be an odd number? Repeated digits are allowed.
2. A witness remembered the following about a license plate. It was one letter followed by
four digits. The letter was not a vowel and the number did not have a zero. How many
such license plates are possible?
3. After a bit of thought the witness in number 2 remembered a bit more about the license
plate. It was one letter followed by four digits. The letter was a vowel, the number did
not have a zero, and number was used more than once. How many such license plates are
4. How many distinct “words” can be made using all letters in “PROBABILITY”?
5. Cathy’s clothing cornucopia sells pure cotton Capris, cotton-polyester Capris, and
polyester Capris. Each comes in four colors and eight sizes. How many choices of Capris
are available?
6. How many ways can a squad of 4 relay runners be chosen from a track team of nine
runners? Due to factors such as efficient baton transfers that the order of the runners
7. The W&W candy company offers customers the opportunity to create their own color
mix of candy. There are 15 colors to choose from and the customer can select up to five
colors without repeating colors. How many ways can a customer select exactly five
colors to be included in the mix?
8. How many ways can two teams of a 16-team league be selected to play each other
without regard to which team is at home?
9. In horse racing, an exacta bet requires the better to pick the first two horses in the exact
order. If there are nine horses in race, in how many ways could you make an exact bet?
10. Assuming a year has 365 days, find the probability that in a group of 30 randomly
selected people at least two have the same birthday.
11. Three students are to be selected from a class that has eight freshman and twelve
sophomores. Find the probability that two sophomores are selected.
12. Five cards are selected from a standard deck of cards. Find the probability that at least on
is face card.
13. After studying all night for final exam, a bleary-eyed student randomly grabs two socks
from a drawer containing eight black, six brown, and four blue socks, all mixed together.
Find the probability that student grabs a matched pair.
14. A fair coin tossed 15 times. Find the probability that it is heads exactly 9 times.
15. A coin is weighted so that P(head) = 0.6 and it is tossed 8 times. Find the probability that
number of head is 5.
16. A survey found that 25.4 % of credit-card-holding families hardly ever pay off the
balance. Find the probability that exactly five families in survey of twenty credit-cardholding families hardly ever pay pf the balance.
17. Define what is meant by a “fair game” in terms of the expected value, E(x).
18. Find E(x)
19. In a small class of twelve students, two did not do the homework. The professor
randomly selected half of the students to present situations to homework problems on the
board. Find the expected value for the number of selected students that did not do the

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