Question

find the value of n such that 5× 4Pn = 6× 5Pn-1.

Answer 1

Answer:

3

Step-by-step explanation:

We have to find the value of n for which 5×⁴$P_{n}$=6×⁵$P_{n-1}$ ....... (1)

Now from the above expression (1) we can write,

$5.\frac{4!}{(4-n)!}=6.\frac{5!}{(5-n+1)!}$ { We can use the formula ⁿPₐ=  $\frac{n!}{(n-a)!}$}

⇒ $5=\frac{6*5}{(5-n)(6-n)}$

⇒(5-n)(6-n)=6

⇒30-11n+n²=6

⇒n²-11n+24=0

⇒(n-8)(n-3)=0

⇒ n=8 or 3.

Now, n can not be 8, because in that case ⁴P₈ or ⁵P₇ will be invalid.

Hence, we have to take the value of n to be 3.

Hence n=3. (Answer)