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

A person writes letters to six friends and addresses the corresponding envelopes. Let x be the number of ways so that at least two of the letters are in wrong envelopes and y be the number of ways so that all the letters are in wrong envelopes, then xy=

A
716
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
454
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
265
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
0
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 454
x: Number of ways of getting 2 wrong OR 3 wrong OR 4 wrong OR 5 wrong OR 6 wrong
y: Number of ways of getting 6 wrong
xy: Number of ways of getting 2 wrong OR 3 wrong OR 4 wrong OR 5 wrong
In general, number of ways of getting r wrong: nCr×r!×(12!13!+14!...(1)r1r!)
Thus, XY=62C×2!×(12!)+63C×3!×(12!13!)+64C×4!×(12!13!+14!)+65C×5!×(12!13!+14!15!)=15+40+135+264=454
Hence, (b) is correct.

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