wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

No. of different ways by which 3 persons A,B and C having 6 one rupee coins, 7 one rupee coins and 8 one rupee coins respectively can donate 10 one rupee coins collectively.

A
41
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
43
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
47
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
49
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 41
We know that, the number of non-negative integral solutions to
x1+x2+...+xn=r is (n+r1Cr)
Hence for A+B+C=10
Total number of ways =10+31C10=12C10
Now, we will have to subtract the cases where A>6,B>7,C>8

CaseI:
A>6,B>0,C>0 Give A=7 already and then find the total non-negative integral solution.
A+B+C=10
Bur, A=A+7
A+B+C+7=10A+B+C=3
Total no. of ways =3+31C3=5C3

CaseII:
A>0,B>7,C>0 ; Similarly as above
A+B+C=2
Total no. of ways =3+21C2=4C2

CaseIII:
A>0,B>0,C>8
A+B+C=1
Total no. of ways =3+11C1=3C1

Total number of ways =12C10(5C3+4C2+3C1)
Hence, correct answer is 41

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Combinations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon