1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# The number of integral solutions of equation x+y+z+t=29, when x≥1,y≥2,z≥3 and t≥0 is

A
2600
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
2500
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2550
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2700
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 2600PROBLEMS BASED ON CERTAIN THEOREMS ON COMBINATIONS :⋅ The number of positive integral solutions of the equation x1+x2+x3+....+xr=n is n−1Cr−1.⋅ The number of non-negative integral solutions of the equation<br>x1+x2+x3+....+xr=n is n+r−1Cr−1.x+y+z+t=29Let x′=x−1,y′=y−2,z′=z−3,t′=t where x′, y′, z′, t′≥0⇒x′+y′+z′+t′=29−1−2−3=23 here n=23, r=4Thus required number of ways is =n+r−1Cr−1=26C3=2600

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Multinomial Theorem
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program