Question

in how many ways can the letter of word 'MONDAY' be arranged? How many of these arrangements do not begin with M? How many begin with M and do not end with Y​

Answer 1

Explanation:

Monday has 6 different letters.

and we have therefore 6 positions to put letters.

so, for the first position we have 6 choices.

for the second position the 5 choices, and so on.

that makes all together

6! = 6×5×4×3×2×1 = 720

ways to arrange the letters.

if the arrangements must not begin with M, we are taking one choice away for the 1st position.

we can express that as all the ways with only 5 choices for the first position, or as the total number of possibilities minus the ones that start with M.

1.

5×5×4×3×2×1 = 600

2.

6! - 1×5! = 720 - 120 = 600

now, for the possibilities that start with M but do not end with Y.

that is the same as demanding that the second position does not have a Y.

so, the first position has only one choice, and the second position has one choice less :

1×4×4×3×2×1 = 96