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).

(a) How many such numbers are there?

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

(c) Pat circles the middle digit of each number, then adds up all the circled digits. What sum does Pat get?

Question

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). 

(a) How many such numbers are there? 

(b) One of Pat's numbers is chosen at random. What is the probability that the tens digit is a 1? 

(c) Pat circles the middle digit of each number, then adds up all the circled digits. What sum does Pat get?

alexwee123 · Answer

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