Question

In how many ways can 6 apples be distributed among 3 boys, there being no restriction to the number of apples each boy may get?729739759749

Answer 1

Answer:

$\textbf{Total number of required ways = }\bf 56$

Step-by-step explanation:

Total number of apples = 6

⇒ n = 6

Number of boys among which the given number of 6 apples needed to be distributed = 3

⇒ r = 3

Now, It is given that there is no restriction to the number of apples each boy may get.

So, Total number of such ways can be easily calculated by using the concept of permutation and the associated formula to finding the number of ways is given by :

$\text{Total number of required ways = }_{r-1}^{n+r-1}_\textrm{P}\\\\\implies \text {Total number of required ways = }_{3-1}^{6+3-1}_\textrm{P}\\\\\implies \text{Total number of required ways = }_{2}^{8}_\textrm{P}\\\\\implies \text{Total number of required ways = }\frac{8!}{6!}\\\\\implies\text{Total number of required ways = }8\times 7\\\\\implies\textbf{Total number of required ways = }\bf 56$

Answer 2

Answer:

Total number of ways=n+r-1 P r-1

=6+3-1 P 3-1

=8P2

=8!/6!

=8×7×6!/6!

=56 ways