wiz-icon
MyQuestionIcon
MyQuestionIcon
4
You visited us 4 times! Enjoying our articles? Unlock Full Access!
Question

A four digit number (numbered from 0000 to 9999) is said to be lucky if sum of its first two digits is equal to the sum of its last two digits. If a four digit number is picked up at random, then the probability that it is a lucky number is:

A
0.07
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
0.067
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
0.67
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
None
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 0.067
Total number of ways of choosing a four digit number from (0000 to 9999) = 104.
Let sum of first two digits and sum of last digits be k then number of ways will be a2k where ak is number
of non – negative integral solutions of the equation x1+x2=k,(0k18)
Then ak = Coefficienent of xk in
(1+x+x2+........+x9)2
Then
(1+x+x2+........+x9)2
=a0+a1x+a2x2+........+a18x18.
a20+a21+........+a218 =constant term in
(a0+a1x+.......+a18x18)(a0+a1x+........+a18x18)
=const. term in (1+x+.......+x9)2(1+1x+....+1x9)2
=Coefficient of x18 in (1+x+x2+....+x9)4
=Coefficient of x18 in (14x10)(1x)4
= coefficient of x18 in (14x10)(1x)4
=21C34.11C3=1330660=670.
Hence, required probability =67010000=0.067

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adaptive Q37
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon