in how many ways can 11 identical ice creams be distributed among 4 girls
Answers
Given : 11 identical ice creams be distributed among 4 girls
To Find : Number of ways
Solution:
11 to 1st girl - 1 way
10 to 1st girl 3 way ( 1 to each )
9 to 1st girl 6 way ( 2 , 0 , 0 - ways ) , ( 1 , 1 , 0 - 3ways)
8 to 1st girl 10 ways ( 3, 0 ,0 - 3 ways) ( 2 , 1 0 - 6 ways ) ( 1, , 1 , 1) 1 way
0 to 1st girl 78 ways
1 way = ²C₂
3 way = ³C₂
6 way = ⁴C₂
10 way = ⁵C₂
²C₂ + ³C₂ + .................................................+ ¹³C₂
= ( 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 )
= 364
364 ways 11 identical ice creams be distributed among 4 girls
Direct formula
Number of ways of distributing n identical things among r persons when each person may get any
number of things =(n+r-1)C(r-1)
= 11+4 - 1= 14
4 - 1= 3
¹⁴C₃ = 364
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