Question

Find the total number of selections of A + B + C + D objects where A are alike (of one kind), B are alike (of second kind), C are alike (of third kind) and D are alike (of fourth kind) if he has to select at least one of each kind of object.

• A. A + B + C + D
• B. (A +1) (B + 1)(C +1) (D+1)
• C.
• D. (A +1) (B + 1)(C +1) (D+1) - 1

Answer 1

The correct option is C

Number of ways of selecting A alike objects = Selecting one of $1^{st}$ kind of objects or Selecting two of $1^{st}$ kind of objects........ Selecting (A- 1) of $1^{st}$ kind of objects or Selecting all A objects of $1^{st}$ kind of objects

Number of ways of selecting at least one of A alike objects = A ways

Similarly,

Number of ways of selecting at least one of B alike objects = B ways

Number of ways of selecting at least one of C alike objects = C ways

Number of ways of selecting at least one of D alike objects = D ways

The total number of selections of A + B + C + D objects if person has to select at least one of each kind of object

$=A\times B\times C\times D$