Prove that ⁿ¯¹Cᵣ + ⁿ¯¹Cᵣ - ₁ ﹦ⁿCᵣ Help thanks 10 points & Best Answer shall be chosen & spammers reported - no spam please
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Answer:
LHS=RHS
Step-by-step explanation:
LHS=
n−1
C
r
+
n−1
C
r−1
=
(n−1−r)!r!
(n−1)!
+
(n−1−r+1)!(r−1)!
(n−1)!
=
(n−r−1)!r(r−1)!
(n−1)!
+
(n−r)!(r−1)!
(n−1)!
r(n−r−1)!(r−1)!
(n−1)!
+
(n−r)(n−r−1)!(r−1)!
(n−1)!
(n−r−1)!(r−1)!
(n−1)!
(
r
1
+
n−r
1
)
(n−r−1)!(r−1)!
(n−1)!
.
r(n−r)
n−r+r
(n−r−1)!(r−1)!
(n−1)!
.
r(n−r)
n
(n−r)!r!
n!
n
C
r
=RHS
LHS=RHS