This is a discrete math (counting techniques) problem. Please explain clearly, no cursive writing. A company has 10 different warehouses for storing their inventory. They will be storing 100identical crates of widgets in the 10 warehouses.(a) How many ways are there for the company to distribute the crates of widgets among thewarehouses?(b) How many ways are there for the company to distribute the crates of widgets among thewarehouses if at least 5 crates must be stored at each warehouse?(c) How many ways are there for the company to distribute the crates of widgets among thewarehouses if at most 50 crates can be stored at any one warehouse?(d) How many ways are there for the company to distribute the crates of widgets among thewarehouses if at most 40 crates can be stored at any one warehouse? Additional InstructionsFor the exercises that ask you to answer "How many ...", express your results as a combinatorialformula, calculate the integer value that answers the question, and provide a short justification ofyour formula choice.

Name: This is a discrete math (counting techniques) problem. Please explain
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: This is a discrete math (counting techniques) problem. Please explain clearly, no cursive writing. A company has 10 different warehouses for storing their inventory. They will be storing 100identical crates of widgets in the 10 warehouses.(a) How man

Given:- A company has 10 different warehouses for storing their inventory. They will be storing 100identical crates of widgets in the 10 warehouses. (a) How many ways are there for the company to distribute the crates of widgets among the warehouses? (b) How many ways are there for the company to distribute the crates of widgets among the warehouses if at least 5 crates must be stored at each warehouse? (c) How many ways are there for the company to distribute the crates of widgets among the warehouses if at most 50 crates can be stored at any one warehouse? (d) How many ways are there for the company to distribute the crates of widgets among the warehouses if at most 40 crates can be stored at any one warehouse?Solution :- (a) No. of .ways for the company to distribute the crates of widgets among the warehouse: 10 warehouse = x i 100 crates identical ∑xi=100 x 1 +x 2 +x 3 +............. +x 10 =100 = 100 +10-1 c 10-1 =109 c 9 b) No.of. ways are there for the company to distribute the crates of widgets among the warehouses if at least 5 crates must be stored at each warehouse: Each x i atleast 5 crates must be present x 1 +x 2 +x 3 +............. +x 10 =100 for x i ≥5 = 50+ 10-1 c 10-1 59 c 9.c) No.of ways are there for the company to distribute the crates of widgets among the warehouses if at most 50 crates can be stored at any one warehouse: x i ≤50 Let p i be the property if x i ≥50 x i ≤50 N p'1p'2.....................p10'= N=∑Np1+∑Np1p2+∑Np1p2p3+.................∑Np1p2......p10 N = number of solution N (p 1) =number of solution for x≥51 N (p 1 p 2) = number of solution for x 1,≥51 x 2≥51 N p'1p'2.....................p10'=109 c9-10*49+10-1 c10-1+0+........+0 = 109 c9-10.58 c9d) No.of. ways are there for the company to distribute the crates of widgets among the warehouses if at most 40 crates can be stored at any one warehouse : On the above part (c) we have similar value. N p'1p'2.....................p10'=109 c9-10*59+10-1 c10-1+10*18+10-1 c10-1+........+0 = 109 c9-1068 c9+10 27c 9