Question

how many ways are there to distribute 17 district object into 7 distinct boxes with
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Answer 1

Answer:

21 * 5¹⁷

720 * 7¹¹

7¹⁷

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 remaining 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 7 distinct objects and put in 7 distinct boxes

= 7 !  ways

= 5040

now we remained with 10 Distinct objects & 7 Distinct boxes

Each object can be placed in 7 ways

so 10 objects can be placed in 7¹⁰  ways

Total ways = 5040 * 7¹⁰

= 720 * 7¹¹

if no conditions then each object can be placed in 7 ways

= 7¹⁷