how many ways can eight letters be arranged into groups of five where order matters and the first two…
how many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen?\n100\n120\n240\n720
Answer
Answer:
B. 120
Explanation:
Step1: Determine remaining letters and positions
We have 8 letters, 2 are chosen. So 6 left for 3 positions.
Step2: Use permutation formula
The permutation formula is $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 6$ and $r=3$.
Step3: Calculate factorial values
$n!=6! = 6\times5\times4\times3\times2\times1=720$ and $(n - r)!=(6 - 3)!=3!=3\times2\times1 = 6$.
Step4: Compute the permutation
$P(6,3)=\frac{6!}{3!}=\frac{720}{6}=120$.