Number of four digit numbers that can be formed using all the digits except zero such that every number has…
Number of four digit numbers that can be formed using all the digits except zero such that every number has exactly 2 distinct digits in it is
189
216
288
504
Solution
Two distinct digits can be choosen out of 9 digits is in ${ }^9 \mathrm{C}_2=36$ ways now we can form $2^4$ different 4 digit numbers from which wecan excludethe two cases
$
\begin{aligned}
& \Rightarrow 36 \times\left(2^4-2\right)=36 \times(16-2) \\
& \Rightarrow 504
\end{aligned}
$