The number of ways of putting 10 different things in 2 boxes such that there are not less than 2 things in any of the two boxes is O (a) 1024 O (b) 1023 (c) 1013 (d) 1002
Answers
Given : putting 10 different things in 2 boxes such that there are not less than 2 things in any of the two boxes
To Find : The number of the ways
Solution:
Total things = 10
number of boxes = 2
Minimum in a box = 2
Hence maximum in a box = 10 - 2 = 8
so in a box things can be
2 , 3 , 4 , 5 , 6 ,7 or 8
Hence number of ways
= ¹⁰C₂ + ¹⁰C₃ + ¹⁰C₄ + ¹⁰C₅ + ¹⁰C₆ + ¹⁰C₇ + ¹⁰C₈
= 45 + 120 + 210 + 252 + 210 + 120 + 45
= 1002
other way :
¹⁰C₂ + ¹⁰C₃ + ¹⁰C₄ + ¹⁰C₅ + ¹⁰C₆ + ¹⁰C₇ + ¹⁰C₈
= 2¹⁰ - ¹⁰C₀ - ¹⁰C₁ - ¹⁰C₉ - ¹⁰C₁₀
= 1024 - 1 - 10 - 10 - 1
= 1002
There are 1002 ways
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