Pat writes all the 7-digit numbers in which all the digits are different and each digit is greater than the one to its right (so the tens digit is greater than the units, the hundreds greater than the tens,

and so on). For example, 9,865,320 is one of the numbers that Pat writes down.

(a) How many numbers does Pat write down?

(b) One of Pat's numbers is chosen at random. What is the probability that the tens digit is a 1?

(c) One of Pat's numbers is chosen at random. What is the probability that the middle (thousands) digit is a 5?

Note: of course, you could solve this problem by repeating Pat's experiment and writing down all of the numbers. But don't do that -- figure out the answers without needing to write down all of the numbers!

Mr.Owl
Nov 4, 2017

#1**+1 **

Can I make this a shorter answer? YES I CAN

Pat writes all the 7-digit numbers in which all the digits are different and each digit is greater than the one to its right (so the tens digit is greater than the units, the hundreds greater than the tens, and so on). For example, 9,865,320 is one of the numbers that Pat writes down.

(a) How many numbers does Pat write down?

9,8,7,6,5,4,3,2,1,0 3 of the 10 must be removed 10C3 = 120

(b) One of Pat's numbers is chosen at random. What is the probability that the tens digit is a 1?

(9,8,7,6,5,4,3,2) 1,0 3 of the 8 must be left out 8C3= 56

P(1 in the 10s column) =

(c) One of Pat's numbers is chosen at random. What is the probability that the middle (thousands) digit is a 5?

(9,8,7,6 one of these four must be left out) 5 ( 4,3,2,1,0 two iof thse 5 must be left out) 4C1*5C2=4*10=40

P(5 is in the middle) =

Lightning
Mar 17, 2018