Question

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if all letters are used but first letter is a vowel?

Answer 1

5×4×3×2×2=240
in 240 ways we can write it

Answer 2

Answer:

240 ways

Step-by-step explanation:

MONDAY:total number of letters :6

since no alphabet is repeated

If first letter must be a vowel:i.e. A,O

means fixed A at the first position as

A _ _ _ _ _

now remaining 5 letters can be arranged from 5 letters remaining

so possible ways are $5 P_{5} \\\\=\frac{5!}{(5-5)!} \\\\\\=\frac{5\times 4\times 3\times 2 \times 1}{0!} \\\\since\:\:\:0!=1\\\\\\=120$

O _ _ _ _ _

now remaining 5 letters can be arranged from 5 letters remaining

so possible ways are $5 P_{5} \\\\=\frac{5!}{(5-5)!} \\\\\\=\frac{5\times 4\times 3\times 2 \times 1}{0!} \\\\since\:\:\:0!=1\\\\\\=120$

so,total possible ways to arrange the letters of MONDAY while fix vowel at first place are=120+120

=240