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vyom
asked
2017-02-01 19:25:48
Ten distinct balls are put into nine indistinguishable boxes so that no box is empty. The number of ways of placing these balls is?
Ten distinct balls are put into nine indistinguishable boxes so that no box is empty. The number of ways of placing these balls is?
permutations & combinations
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jiju (Junior Maths Expert, careerbless.com)
answered
2017-02-01 19:49:58
Solution 1
Select any two balls and place in any of the box. $10\text{C}2$ ways. Remaining eight balls can be placed in the remaining eight boxes like one ball in each box.
Required number of ways $=10\text{C}2=45$
Solution 2
See
formula 11
Required count $=S(10,9)=\dbinom{10}{2}=45$
<b>Solution 1</b><br><br>Select any two balls and place in any of the box. $10\text{C}2$ ways. Remaining eight balls can be placed in the remaining eight boxes like one ball in each box.<br><br>Required number of ways $=10\text{C}2=45$<br><br><b>Solution 2</b><br><br>See <a href="/aptitude/qa/permutations_combinations_imp7.php#1" target="_blank">formula 11</a> <br><br>Required count $=S(10,9)=\dbinom{10}{2}=45$
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