i) If 15 ! + 16 ! = 8 !, find x , (ii) Find r, if 5 4 = 6 5−1
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1
Answer:
Given that: 5
4
P
r
=6
5
P
r−1
We know,
n
P
r
=
(n−r)!
n!
Now, we can rewrite the above given equation as:
5×
(4−r)!
4!
=6×
[5−(r−1)]!
5!
(4−r)!
5!
=
(6−r)!
6×5!
⇒
(4−r)!
1
=
(6−r)(5−r)(4−r)!
6
(6−r)(5−r)=6 ⇒r
2
−11r+24+0 ⇒(r−8)(r−3)=0
∴r=3 or r=8 But [r=8 has no meaning since r>n]
Hence, r=3
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