We have boxes of three colors white, black and gray and 10 balls of three colors– again white, black and gray. All the balls of same color are assumed to be identical. We have the following constraints: 1. No box contains a ball that has same color as the box. 2. No box is empty 1 In how many ways can we arrange these 30 balls into boxes if: (a) No constraint is to be satisfied. (b) Constraint 1 is satisfied. (c) Constraint 2 is satisfied. (d) Constraint 1 and 2 are satisfied.
We have boxes of three colors white, black and gray and 10 balls of three colors– again white, black and gray. All the balls of same color are assumed to be identical. We have the following constraints: 1. No box contains a ball that has same color as the box. 2. No box is empty 1 In how many ways can we arrange these 30 balls into boxes if: (a) No constraint is to be satisfied. (b) Constraint 1 is satisfied. (c) Constraint 2 is satisfied. (d) Constraint 1 and 2 are satisfied.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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We have boxes of three colors white, black and gray and 10 balls of three colors– again white, black
and gray. All the balls of same color are assumed to be identical. We have the following constraints:
1. No box contains a ball that has same color as the box.
2. No box is empty
1
In how many ways can we arrange these 30 balls into boxes if:
(a) No constraint is to be satisfied.
(b) Constraint 1 is satisfied.
(c) Constraint 2 is satisfied.
(d) Constraint 1 and 2 are satisfied.
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