Please answer the following questions Leave brief explanatio

Please answer the following questions. Leave brief explanation of the answers.

Question 1 (

A local BBQ restaurants offers 2 side dishes with a lunch plate. There are 7 side dishes. How many choices of side dishes does a customer have? Note: There is no requirement that the customer chooses different side dishes (i.e. he or she can choose say baked beans twice as their side dish).

Question 1 options:

42

14

49

28

Question 2

A student club with 30 members need to chose officers. There are five officer positions and no member can occupy two positions at the same time. How many possible slates of candidates are there?

Question 2 options:

30!/(5!25!)

25!/30!

30!/5!

30!

Question 3

Both bridge and poker are played with 52 cards. A poker hand consists of 5 cards; a bridge hand of 13. Are there more possible poker hands or bridge hands?

Question 3 options:

Poker

Bridge

Neither. They are both the same

Can\'t be done with the information given.

Question 4 (1 point)

License plates in the great state of Utah consist of 2 letters and 4 digits. Both digits and letters can repeat and the order in which the digits and letters matter. Thus, AA1111 and A1A111 are different plates. How many possible plates are there? Justify your answer.

Question 4 options:

26x15x10x9x8x7x6

26x26x10x10x10x10

26x26x10x10x10x10x15

6!/(2!4!)

Question 5

Like in Utah, license plates in the great state of Wisconsin consist of 2 letter and 4 digits. However, only digits can repeat and the two letters always precede the digits. How many possible plates are there in Wisconsin?

Question 5 options:

26x26x10x10x10x10

26x25x10x10x10x10

26x26x10x9x8x7

26x25x10x9x8x7

A.	42
B.	14
C.	49
D.	28

Solution

Solved the first three problem, post one more question to get the remaining two problems

Question 1:

The correct answer is Option C (49)

Reason: Since the repetition is allowed, i.e. the first side dish can be choosed in 7 ways (1 side dish out of any 7 possible side dishes)

Second dish can also be choosen in 7 ways, since the first dish can be same as the second dish as given in the problem

Total Number of Ways = 7 (choosing first dish) * 7 (choosing second dish) = 49 ways

Question 2:

The five position can be filled out of 30 possible candidates in 30P5 ways assuming that the combination is specific i.e. one person is defined for the job

Hence the correct answer will be 30!/5!, which is Option C

Question 3:

Number of Poker hands = 52C5 (selecting any five cards from pack of 52 cards)

Number of bridge hands = 52C13(selecting any 13 cards from pack of 52 cards)

Since 52C13 > 52C5

Hence the number of bridge hands will be more

Therefore the correct answer is Option B