{"id":90557,"date":"2025-06-01T10:30:58","date_gmt":"2025-06-01T10:30:58","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90557"},"modified":"2025-06-01T10:30:58","modified_gmt":"2025-06-01T10:30:58","slug":"the-number-of-ways-by-which-6-distinct-balls-can-be-put-in-5-distinct","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-number-of-ways-by-which-6-distinct-balls-can-be-put-in-5-distinct\/","title":{"rendered":"The number of ways by which 6 distinct balls can be put in 5 distinct"},"content":{"rendered":"

The number of ways by which 6 distinct balls can be put in 5 distinct boxes are<\/p>\n

[amp_mcq option1=”7776″ option2=”15625″ option3=”720″ option4=”120″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2020<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
15625<\/section>\n
This is a problem of placing distinct objects into distinct containers. For each distinct object, there are multiple independent choices of container.<\/section>\n
We have 6 distinct balls and 5 distinct boxes.
\nConsider the balls one by one:
\nThe first ball can be put into any of the 5 distinct boxes (5 choices).
\nThe second ball can be put into any of the 5 distinct boxes (5 choices).
\n…
\nThe sixth ball can be put into any of the 5 distinct boxes (5 choices).
\nSince the choice for each ball is independent, the total number of ways is the product of the number of choices for each ball.
\nTotal ways = $5 \\times 5 \\times 5 \\times 5 \\times 5 \\times 5 = 5^6$.
\n$5^6 = 15625$.
\nThis is the general formula for placing $n$ distinct items into $m$ distinct bins: $m^n$. Here $n=6$ and $m=5$, so $5^6$.<\/section>\n","protected":false},"excerpt":{"rendered":"

The number of ways by which 6 distinct balls can be put in 5 distinct boxes are [amp_mcq option1=”7776″ option2=”15625″ option3=”720″ option4=”120″ correct=”option2″] This question was previously asked in UPSC CAPF – 2020 Download PDFAttempt Online 15625 This is a problem of placing distinct objects into distinct containers. For each distinct object, there are multiple … <\/p>\n

Detailed SolutionThe number of ways by which 6 distinct balls can be put in 5 distinct<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1288,1102],"class_list":["post-90557","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1288","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe number of ways by which 6 distinct balls can be put in 5 distinct<\/title>\n<meta name=\"description\" content=\"15625 This is a problem of placing distinct objects into distinct containers. 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