(1) Show that, "C,
n-r+1.
n
"C, 1
Answers
Answered by
1
Answer:
=
(n−r)!r!
n!
+
(n−r+1)!(r−1)!
n!
=n![
(n−r)!r!
1
+
(n−r+1)!(r−1)!
1
]
=n![
(n−r)!r(r−1)!
1
+
(n−r+1)!(r−1)!
1
]
=
(r−1)!
n!
[
(n−r)!r
1
+
(n−r+1)!
1
]
=
(r−1)!
n!
[
r(n−r)!
1
+
(n−r+1)(n−r)!
1
]
=
(r−1)!(n−r)!
n!
[
r
1
+
(n−r+1)
1
]
=
(r−1)!(n−r)!
n!
[
r(n−r+1)
n−r+1+r
]
=
(r−1)!(n−r)!
n!
[
r(n−r+1)
n+1
]
=
(n−r+1)(r−1)!r(n−r)!
(n+1)n!
=
(n−r+1)!r!
(n+1)!
=
n+1
C
r
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