Number of 6 – digit numbers such that
i) the digits of each number are all from the set  $\{3,4,5,6,7\}$
ii) any digits that appears in the number appears at least twice.
The number of such numbers formed is____

Case (i) all digits are same : ${ }^5{C}_1$
Case (ii) three digits appear twice each : ${ }^5{C}_3.\frac{6!}{2!2!2!}$
Case (iii) two digits appear thrice each : ${ }^5{C}_3.\frac{6!}{3!3!}$
Case (iv) one digits appear four times and one digit twice  ${ }^5{C}_2.\frac{6!}{4!2!}{}^2{C}_1$
Number of ways  $=5+900+200+300=1405$