nPr÷n-1Pr-1 is equal to??
Answers
Answered by
0
Answer:
Please mark as brealient
Step-by-step explanation:
L.H.S. =
n
P
r
=
(n−r)!
n!
..(1)
R.H.S. =
n−1
P
r
+r.
n−1
P
r−1
=
(n−r−1)!
(n−1)!
+
(n−r)!
(n−1)!
=
(n−r−1)!
(n−1)!
[1+
n−r
r
]
=
(n−1).(n−r−1)!
n.(n−1)!
=
(n−r)!
n!
..(2)
Hence from (1) and (2)
n
P
r
=
n−1
P
r
+r.
n−1
P
r−1
.
Similar questions