sandy wrote:
The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3rd letter in the list and H is not next to G. How many such rearrangements are
A. 60
B. 36
C. 24
D. 12
E. 6
Another approach:
Take the task of arranging the 7 digits and break it into
stages.
We’ll begin with the
most restrictive stages.
Stage 1: Place the letter G
Since the letter G
must be placed in the 3rd position, we can complete stage 1 in
1 way
Stage 2: Place the letter H
So far we have: _ _ G _ _
Since H cannot be next to G, we can only place H in the 1st position or the 5th position
So we can complete this stage in
2 ways.
Stage 3: Place the letter I
We can place I wherever we wish.
There are 3 spaces remaining, so we can complete this stage in
3 ways.
Stage 4: Place the letter J
We can place I wherever we wish.
There are 2 spaces remaining, so we can complete this stage in
2 ways.
Stage 5: Place the letter K
There is 1 space remaining, so we can complete this stage in
1 way.
By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus arrange all 5 letters) in
(1)(2)(3)(2)(1) ways (= 12 ways)
Answer: D
Cheers,
Brent
I liked ur explanation.
the first blank I can use H I J K, the second I can use any of ( J I K ), then G , then any of the rest except H, then the remaining.