Number of non-negative integral solutions of the in-equation $20 \leq x + y + z < 26$ are

^{28} C_{2} -^{23} C_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

^{28} C_{3} -^{22} C_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

^{28} C_{5} -^{23} C_{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

^{28} C_{3} -^{22} C_{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

^{28} C_{5} -^{23} C_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $^{28} C_{3} -^{22} C_{3}$
$20 \leq x + y + z < 26$
$x + y + z = 20, 21, 22, 23, 24, 25$
Hence number of solutions $=^{22} C_{2} +^{23} C_{2} +^{24} C_{2} +^{25} C_{2} +^{26} C_{2} +^{27} C_{2}$
$= (^{22} C_{3} +^{22} C_{2} +^{23} C_{2} +^{24} C_{2} +^{25} C_{2} +^{26} C_{2} +^{27} C_{2}) -^{22} C_{3}$ $=^{28} C_{3} -^{22} C_{3}$

Suggest Corrections