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Fully explain your answers for all questions. Q2. A digit number is called monotone if its...

Fully explain your answers for all questions.

Q2. A digit number is called monotone if its digits form a strictly increasing sequence. For example, 123 is monotone while 321 and 223 are not.

(a) How many monotone numbers with three digits (from 100 to 999) exist?

(b) How many monotone numbers with three digits are divisible by 5?

(c) How many monotone numbers with three digits are divisible by 2?

(d) Use the principle of inclusion-exclusion to work out how many four digits number are neither monotone, nor divisible by 5, nor divisible by 2.

Math   Statistics-And-Probability   
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