Explanation
first place should be occupied by either 3 or 4.
Case 1 : First place is occupied by the digit 4
4 _ _ _
now in the set from where we can pick numbers is left with ={2,2,3,3,3,4,4,4}
if we got 3 of each digit(which are 2,3 and 4) then number of ways by each of those blanks can be
filled in are 3 coz we have 3 choices of digits: pick 2,3 or 4.
But we do not have just enough 2′s to fill all those 3 spaces with the digit 2.
∴ we need to subtract this case where number would be 4222.
So, total numbers obtained using the numbers in our current set =1×3×3×3−1=26.
The first one is for the digit 4, coz its fixed for this case; the subtracted one is for the case 4222 that can't be made possible.
Case 2: First place is occupied by the digit 3
3 _ _ _
now in the set from where we can pick numbers is left with ={2,2,3,3,4,4,4,4}
we have enough 4′s here but lack 3′s and 2′s ∴, the cases we need to subtract are 3222 and 3333
So, total numbers obtained using the numbers in our current set =1×3×3×3−2=25
both cases are independently capable of giving us the answer, we have =26+25=51.
Hence answer is option B.