Question

How many ways are there to distribute 17 distinct objects into 7 distinct boxes with:
(i) At least two empty box (ii) No empty box

Answer 1

Answer:

At least two empty box = 21 * 5¹⁷

No empty box = 24 * 5¹³

Step-by-step explanation:

17 distinct objects into 7 distinct boxes

(i) At least two empty box

First select two empty boxes from 7 boxes

⁷P₂ = 21

Now 17  distinct object in 5 distinct boxes

Each object can be placed in 5 ways

so 17 objects can be placed in 5¹⁷  ways

Total ways = 21 * 5¹⁷

(ii) No empty box

First take 5 distinct objects and put in 5 distinct boxes

= 5 !  ways

= 120

now we remained with 12 Distinct objects & 5 Distinct boxes

Each object can be placed in 5 ways

so 17 objects can be placed in 5¹²  ways

Total ways = 120 * 5¹²

= 24 * 5¹³