intro to stats 4.4 combinations and permutations

You need to have a password with 5 letters followed by 2 odd digits between 0 and 9, inclusive. If the characters and digits cannot be used more than once, how many choices do you have for your password?

157872000 5 letters from 26 options; 26*25*24*23*22= 7893600 2 odd numbers from 5 options; 5*4=20 7893600*20= 157872000

There are 16 people in an office with 6 different phone lines. If all the lines begin to ring at once, how many groups of 6 people can answer these lines?

16C6= 8008 (order does not matter, so combination is used) *use calculator MATH>PROB>nPr then enter n & r n=16, r=6

Evaluate the following expression. 8!/5!

336 *use calculator, enter 8 then go to MATH>PROB>4:!

The newly elected president needs to decide the remaining 5 spots available in the cabinet he/she is appointing. If there are 11 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?

55440 11P5=55440

A doctor visits her patients during morning rounds. In how many ways can the doctor visit 7 patients during the morning rounds?

7!= 5040

Evaluate the following: 13! / 4! (13-4)!

715

Evaluate the following expression. Express your answer as a fraction or a decimal number rounded to four decimal places. 11C8/11P6

1/2016 or 0.0005

A coordinator will select 5 songs from a list of 10 songs to compose an event's musical entertainment lineup. How many different lineups are possible?

10P5= 30240 (order matters, so permutation is used) *use calculator MATH>PROB>nPr then enter n & r n=10, r=5

How many ways can Rudy choose 6 pizza toppings from a menu of 14 toppings if each topping can only be chosen once?

14C6= 3003 *use calculator MATH>PROB>nCr then enter n & r n=14, r=6

Evaluate the following expression. 9P5

15120 *use calculator MATH>PROB>nPr then enter data

You are ordering a hamburger and can get up to 7 toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get 3 toppings? Express your answer as a fraction or a decimal number rounded to four decimal places.

35/128 or 0.2734

In how many ways can the letters in the word 'Treatment' be arranged?

9! (3!*2!)= 30240 9 letters total; 3 t's and 2 e's

Evaluate the following expression. Express your answer as a fraction or a decimal number rounded to four decimal places. 10P7/10C5

2400 *use calculator to get 10P7= 604800 10C5= 252 604800/252= 2400