How many integers are there between 0 and 10,000 with exactly two 3's as digits?

In two digits only one number namely 33

In three digits 33 with any one of the 9 digits. That can be permuted in3 ways . So there are 27 numbers.

In four digits 9* 8 digits with the remaining digits. That can be permuted in 4!/(2! 1! !!)= 12 ways.

There can be 33 withtheother digit also with repetition. 9 of the remaining digits. That can be permuted in 4!/(2! 2!) =6

9*8*12+ 9*6 = 72*12+54 = 864+54 =918

There are 918 four digited number with 33

There are 27 three digited numbers with 33

There is 1 two digited number 33.

Thus 918+27+1 = 946 numbers between 0 and 10,000 with exactly tow 3’ s as digits

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