I need with these problems.

Question

1) Winning the jackpot in the Connecticut Classic Lotto requires  that you choose six different numbers 1 to 44 and your numbers must match the same six numbers that are later drawn.  The order of the selected numbers does not matter. If you buy one ticket, what is the probability of winning the jackpot?

2) In the Maine Megabucks game, you win the jackpot by selecting five different whole numbers from 1 through 41 and getting the same five numbers (in any order) that are later drawn. What is the probability of winning a jackpot in this game?

3) The Teknomill Corporation must appoint a president, chief executive officer (CEO) and chief financial officer (CFO). It must also appoint a Planning Committee with four different members. They are 12 qualified candidates, and officers can also serve on the committee.

How many different ways can the committee be appointed 

4) The typical combination lock uses three numbers between 0 and 49, and they must be selected in the correct sequence. How many different "combinations" are possible 

5) How many different ways can you touch two or more fingers to each other on one hand?

6) DNA is made of nucleotides. Each nucleotide can contain any one of these nitrogenous bases: A,G,C,T. If one of those four bases (A,G,C,T) must be selected three times to form a linear triplet, how many different triplets are possible? All four bases can be selected for each of the three components of the triplet.

 

Answer 1

6)

Step 1:

Four kinds of bases in each nucleotide are .

Number of ways of choosing one of four bases is = 4

To form a linear triplet the selection is made for three times.

The Total number of triplets

Solution:

Possible triplets are .

Answer 2

(5)

Step 1:

Number of fingers on one hand is 5.

They are = { Thumb = T, Index = I , Middle = M, Ring = R, Pinkie = P }.

The possible cases to touch two fingers to each other on one hand is { TI, TM, TR, TP ; IM, IR, IP ; MR, MP ; RP }.

The number of ways that two fingers touch each other on one hand is 10.

The possible cases to touch three fingers to each other on one hand is { TIM, TIR, TIP; IMR, IMP; MRP, TMR, TRP, IRP, TMP }.

The number of ways that three fingers touch each other on one hand is 10.

The possible cases to touch four fingers to each other on one hand is { TIMR,TIMP, TIRP, TMRP, IMRP }.

The number of ways that four fingers touch each other on one hand is 5.

And finally the possible cases to touch all five fingers to each other on one hand is TIMRP.

The number of ways that all fingers touch each other on one hand is 1.

 

Therefore, the total number of ways that two or more fingers to each other on one hand = 10+10+5+1 = 26.

Solution :

The total number of ways that two or more fingers to each other on one hand is 26.

Answer 3

(3)

Step 1:

The Teknomill Corporation needs to appoint candidates for committee of four members.

There are 12 qualified candidates are available to appoint.

Number of ways 4 members selected from a qualified candidates is .

Solution :

Number of ways of appointing candidates for committee is 495.

Answer 4

(4)

Step 1:

The typical  locking system has a 3 numbers.

The numbers are between 0 to 49.

Number of ways of choosing one of the number is .

To form a correct sequence the selection is made for three times.

The Total number of sequences are .

= 125000

Solution:

Total Possible sequences are 125000.

Answer 5

(2)

Step 1:

Number of ways selecting five different whole numbers from 1 to 41 is .

To win the jackpot one must have to select the same whole numbers from 1 to 41 not necessary in same order.

Again number of ways selecting five different whole numbers from 1 to 41 is .

So the total number of ways is .

= 749398 * 739398

= 561597362404

So the total number ways are 561597362404 .

Winning a jackpot means , one must have to select the same 5 numbers .

There is only one case to select the same five numbers.

The probability of winning the jackpot is

Solution:

The probability of winning jackpot is .