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Formation of Number

(Q).How many 5 digit numbers are there?
Solution:-

9 10 10 10 10ways ways ways ways waysnot 0

= 9×10×10×10×10
= 90000 Answer

(Q). How many 4 digit numbers can be formed from the digit 0, 1, 3, 6, 7, 9
        (i) if repetition of digit is not allowed
        (ii) if repetition of digit is allowed
Solution:- 

5 5 4 3not zero= 5×5×4×3= 300 Answer(ii)(i)5 6 6 6not zeronot zero= 5×6×6×6= 1080 Answer

(Q). Find the number of 5 digit numbers that can be formed from the digits: 6 6 6 9 9.
Solution:-     =  \frac{{5!}}{{3!2!}}

                           = 10 Answer

(Q). Find the nuumber of 5 digit numbers that can be formed from the digit 1 1 6 6 6 such that the number is divisible by 4.
Solution:-

A number is divisible by 4 ⇒ if last two digits of the number is divisible by 4
Hence

1 6 6 1 6

=  \frac{{3!}}{{2!}}
= 3 Answer