Question

The number of ways in which 7 different things can be distributed among 4 persons, when each can receive as many as given, is
A. \[{7^4}\]
B. \[^7{P_4}\]
C.\[^7{C_4}\]
D. \[{4^7}\]

Answer 1

Hint: According to the question, read the statement and convert them in a mathematical way. As, 7 different things can be distributed among 4 persons in 7 different ways.

Complete step-by-step answer:
Given Points:
7 different things
4 persons
Each can receive as many as
So, each different things can be given to 4 person in 7 different ways that is:
So, here we will calculate the number of ways which is equal to 7 times 4 as 7 different things are to be distributed among 4 persons.
Number of ways = \[4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4\]
Hence, number of ways comes out to be \[{4^7}\]
So, option (D) \[{4^7}\] is correct.

Additional Information:
These types of questions are from permutation and combination. We can use the formulas of permutation and combination to calculate the result. As Permutation is only used when we have to follow the order of the given numbers means it is without replacement and combination is used when we don’t have to follow the order of the given numbers. So, the formulas of permutation and combinations are \[^n{P_r} = \dfrac{{n!}}{{\left( {n - r} \right)!}}\] , \[^n{C_r} = \dfrac{{n!}}{{\left( {n - r} \right)!r!}}\] respectively. Here, n is the total number of items or objects and r is the objects or items that are taken or required.

Note: In these types of questions, we see whether the permutation or combinations occurs and use the formula accordingly. Some types of questions can be directly solved by just converting and understanding the statements in a practical way.