Question

The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is \;?

• A. \(1292\)
• B. \(1296\)
• C. \(1290\)
• D. \(4090\)

Hint:

“No person gets all 4” is a classic use of complementary counting: total minus the ways that violate the condition.

Answer 1

The Correct Option is C

Step 1: Total distributions without restriction.
Each of the 4 distinct items can go to any of 6 persons, so there are \[ 6^4 \;=\; 1296 \] possible ways in total. Step 2: Subtract the disallowed cases (where one person gets all 4).
There are exactly 6 ways in which one particular person receives all 4 objects. Hence \[ \text{disallowed} = 6. \] Therefore, the valid count is \[ 1296 - 6 = \boxed{1290}. \]