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) =