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

If 12 persons are seated in a row, the number of ways of selecting 3 persons from them, so that no two of them are seated next to each other is

A
85
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
100
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
120
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
240
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 120
Given that 12 persons are sitting in a row,
Let us choose 3 persons in a random way,so the remaining persons are 9,
let w be the number of persons sitting left to the first person,
let x be the number of persons sitting in between the first and second person,
Let y be the number of persons sitting between the second and third person,
Let z be the number of persons sitting right to the third person,
so,w+x+y+z=9,
but no two persons should be next to each other,
y,z1,
let y=a+1 and z=b+1,
The equation now turns to,
w+a+b+z=7,
the number of ways of selecting 3 persons such that no 2 are sitting next to each other is the number of solutions to the above equation,
i.e.,(7+4141)=(103)=120


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Combinations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon