Question

How many 2 digit number are there using1,4,5,7,8,9

Answer 1

If digits can be repeated: 36

If the digit can not be repeated: 30

Explanation:

If digits can be repeated:

On the first and second place we have 6 digits to choose from.

Therefore we have 6 · 6 = 36 two-digit numbers.

`\begin{array}c11&41&51&71&81&91&&\to6\\14&44&54&74&84&94&&\to6\\15&45&55&75&85&95&&\to6\end{array}\\\vdots\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad6\\\begin{array}c19&49&59&79&89&99&&\to6\end{array}\\.\\.\qquad\qquad\ \ \ \ 6`

If the digit can not be repeated:

On the first place we have 6 digits to choose from and on the second place we have 5 digits to choose from.

Therefore we have 6 · 5 = 30 two-digit numbers.

Answer 2

There may be 30 numbers

Explanation:

There is a formula in permutation for filling 'n' places with 'm' numbers given as mPn i.e, m!/(m-n)!.

Here m=6.

n=2

so the answer will be 6!/4!=30

So 30 2-digit numbers can be formed using 1,4,5,7,8,9