MyQuestionIcon

1

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

Combination

Simplify: 3...

Question

Simplify: ${^{34} C}_{5} + \sum_{r = 0}^{4} {^{(38 - r)} C}_{4}$ .

A

^{38} C_{4}

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

B

^{39} C_{4}

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

C

^{38} C_{5}

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

D

^{39} C_{5}

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

Open in App

Solution

The correct option is B $^{39} C_{5}$
$^{34} C_{5} + 4 \sum r = 0$ $^{38 - r} C_{4}$
$=^{34} C_{5} +^{38} C_{4} +^{37} C_{4} +^{36} C_{4} +^{35} C_{4} +^{34} C_{4}$
$= (^{34} C_{5} +^{34} C_{4}) +^{35} C_{4} +^{36} C_{4} +^{37} C_{4} +^{38} C_{4}$
$=^{35} C_{5} +^{35} C_{4} +^{36} C_{4} +^{37} C_{4} +^{38} C_{4}$ (Using $^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$ )
$=^{36} C_{5} +^{36} C_{4} +^{37} C_{4} +^{38} C_{4}$
$=^{37} C_{5} +^{37} C_{4} +^{38} C_{4}$
$=^{38} C_{5} +^{38} C_{4}$
$=^{39} C_{5}$

Suggest Corrections

thumbs-up

0

Similar questions

^{34} C_{5} + 4 \sum r = 0^{(38 - r)} C_{4}

^{34} C_{5} + 4 \sum r = 0^{38 - r} C_{4}

Q. Using laws of exponents, simplify and write

3^{2} \times 3^{4} \times 3^{8}

Q. Simplify and write the answer in exponential form:

3^{2} \times 3^{4} \times 3^{8}

Q. Using laws of exponents, simplify and write the answer in exponential form :

3^{2} \times 3^{4} \times 3^{8}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Combinations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon