SeoulAtNight
contestada

In how many ways can you spell the word ROOM in the grid below? You can start on any letter R, then on each step you can step one letter in any direction (up, down, left, right, or diagonal).

In how many ways can you spell the word ROOM in the grid below You can start on any letter R then on each step you can step one letter in any direction up down class=

Respuesta :

ArabellaRose25

Answer:

  84? Not sure but pretty sure

Step-by-step explanation:

In a straight line, the word can only be spelled on the diagonals, and there are only two diagonals in each direction that have 2 O's.

If 90° and reflex turns are allowed, then the number substantially increases.

Corner R: can only go to the adjacent diagonal O, and from there to one other O, then to any of the 3 M's, for a total of 3 paths.

2nd R from the left: can go to either of two O's, one of which is the same corner O as above. So it has the same 3 paths. The center O can go to any of 4 Os that are adjacent to an M, for a total of 10 more paths. That's 13 paths from the 2nd R.

Middle R can go the three O's on the adjacent row, so can access the three paths available from each corner O along with the 10 paths available from the center O, for a total of 16 paths.

Then paths accessible from the top row of R's are 3 +10 +16 +10 +3 = 42 paths. There are two such rows of R's so a total of 84 paths.

There are 52 ways to make the word ROOM out of this grid.

What is permutation?

A method of ordering or arranging a group of things, especially one of several possible variations.

Let's start from the Leftmost R:

For the leftmost R there is only 1 way to make the word ROOM.

For the R right to the previous R:

For this R there are 6 possibilities to make the word ROOM.

For the Middle R:

There are 12 ways for the middle R to make the word Room.

Now there are 2 middle R's , 4 leftmost R's and rest 4 R's.

Total possibilities = 2 * 12 + 6 *4 + 4 * 1 = 52 ways

Hence there are 52 possibilities to make the word ROOM.

Learn more about permutation on:

https://brainly.com/question/1216161

#SPJ2

Otras preguntas

Q&A Education