Correct Answer - C
`(c )` Case I : All six digits alike
i.e. `111111`, `222222`……..etc. `=5` ways
Case II : `2` alike `+2` other alike.
Select any three in `"^(5)C_(3)`...
Correct Answer - B
`(b)` Required number of numbers `="(n)C_(0)(2)^(n)+"(n)C_(2)(2)^(n-2)+…`
We know that
`(1+x)^(n)+(x-1)^(n)=2sum_(k=0)^(n)"(n)C_(k)x^(k)`
Hence, put `x=2`, get the result
`2["^(n)C_(0)(2)^(n)+^(n)C_(2)(2)^(n-2)+^(n)C_(2)(2)^(n-4)+^(n)C_(6)(2)^(n-6)+...]`