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

In how many ways the sum of upper faces of four distinct dice can be six ?

A
10
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
84
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
56
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None of these
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 10
Let the digit appears on the top face of dice is x1,x2,x3,x4
Here,number of required ways will be equal to the number of solution of x1+x2+x3+x4=6, x1,x2,x3,x41
Let X1=x11,X2=x21,X3=x31,X4=x41
X1+X2+X3+X4=6(1+1+1+1)=2
where X1,X2,X3,X40
So number of solution is = 2+41C41
= 5C3
=10

Alternate Solution:
For sum of outcomes to be 6 on the dice
the possible quadruplet of outcomes will
(1,1,1,4) & (1,1,2,2)
So number of possible outcome
=4!3!+4!2!×2!=10

flag
Suggest Corrections
thumbs-up
4
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon