9. 2n (2) for for n ≥ 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you please help with #9? Please don't copy the answer from Chegg as it is wrong. TIA

Transcribed Image Text:Justify the equations in 6-9 either by deriving them from for-
mulas in Example 9.7.1 or by direct computation from Theo-
rem 9.5.1. Assume m, n, k, and r are integers.
6. (m+k₁) -
= m + k, for m+k≥ 1
1
n+3
7. (+³)
=
(n+3)(n+2)
2
, for n ≥ -1
n+1
8.
(7) = 1, for k-r≥0
k
r
2n
9.
(²2)
for n ≥ 0
n

Transcribed Image Text:Theorem 9.5.1
The number of subsets of size r (or r-combinations) that can be chosen from a set
of n elements, ("), is given by the formula
P(n,r)
=
first version
r!
or, equivalently,
n!
(-)-
second version
r!(n-r)!
where n and r are nonnegative integers with r ≤n.
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