In how many way can 7 identical balls be placed in 4 boxes, A, B, C and D such that boxes C and D have at least one ball each?

<p><span lang="EN-IN">a + b + c + d = 7 </span></p><p><span lang="EN-IN">a </span><span lang="EN-IN">³</span><span lang="EN-IN"> 0, b</span><span lang="EN-IN">³</span><span lang="EN-IN"> 0, c </span><span lang="EN-IN">³</span><span lang="EN-IN"> 1, d </span><span lang="EN-IN">³</span><span lang="EN-IN"> 1</span></p><p><span lang="EN-IN"> (a, b, c, d are the numbers of balls)</span></p><p><span lang="EN-IN">Let c = c'</span><span lang="EN-IN"> + 1 = 0, 0 ≤</span><span lang="EN-IN">&nbsp;c'</span> <span lang="EN-IN">≤</span><span lang="EN-IN"> 5</span></p><p><span lang="EN-IN">d = d'</span><span lang="EN-IN"> + 1 = 0, 0 </span><span lang="EN-IN">≤</span><span lang="EN-IN"> d'</span> <span lang="EN-IN">≤</span><span lang="EN-IN"> 5</span></p><p><span lang="EN-IN">a + b + c'</span><span lang="EN-IN"> + d'</span><span lang="EN-IN"> = 5</span></p><p><span lang="EN-IN">Numbers of solution = ^{5 + 4 – 1}C_4–1</span></p><p><span lang="EN-IN">= ⁸C₃ = 56</span></p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment