Challenging Prob/Stats questions I am stuck on

Question

Q1: A history pop quiz has one question in which students are asked to arrange the following presidents in chronological order: Hayes, Taft, Polk, Taylor, Grant, and Pierce.

After carefully reading the scenario, determine the number of possible different arrangements of the presidents. Which will work better to determine this answer, permutation or combination? Make an argument as to why your way works.

Besides your method, is there another method to determine the number of outcomes? Explain.

Calculate the probability that an unprepared student will guess the correct order. Explain.

Q2: In a Match 6 Lotto, winning the jackpot requires that you select six different numbers from 1 to 49, and that the same six numbers be drawn in the lottery. The winning numbers can be drawn in any order.

After carefully reading the scenario, determine the number of possible arrangements of the six numbers. Which will work better to determine this answer, permutation or combination? Justify your answer.

Besides your method, is there another method to determine the number of outcomes? Explain.

Calculate the probability of winning. Explain.

Make an argument for or against playing the lottery.

Q3: A classic counting problem in statistics is to determine the number of different ways that the letters of “Mississippi” can be arranged.

After carefully reading the scenario, determine the number of possible different arrangements of the letters of the word “Mississippi.” Which will work better to determine this answer, the fundamental counting rule or the permutations rule? Justify your answer.

Thanks for any help! These have been very challenging for me to understand.

Answer 1

Q1: Since order matters, permutations would be used. The number of arrangement of 6 items taken all together is 6! = 720. The probability that one student would get the correct order is 1/720.

Q2: Since order does not matter you would determine how many combinations of 6 numbers can be drawn from 49 = 49!/(43!6!) = 13983816. The probability winning the lottery is 1/13983816. That probability is a good argument against playing the lottery.

Q3: Mississippi

11 letters

i appears 4 times

s appears 4 times

p appears 2 times

You would use the permutations to find the number of ways to arrange 11 letters taken 11 at a time, however, to account for the repetition of letters, you divide by 4! for both i and s appearing 4 times and 2! for p appearing 2 times to eliminate duplicate possibilities.

11!/ (4!4!2!) = 34,650