How many words can be made from the letters of the word $M O N D A Y$ assuming that no letter is repeated if $4$ letters are used at a time

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Solution

Total no of letters $= 6$

No of letters used at a time $= 4$

No of ways $=^{6} C_{4}$

$\frac{6!}{4! 2!} = \frac{6 \times 5 \times 4!}{4! \times 2} = 15$

No of ways of using $4$ letters $= 4! = 4 \times 3 \times 2 = 24$

The total no of ways $= 15 \times 24 = 360$

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Q. How many words, with or without meaning can be made form the letter of the word MONDAY, assuming that no letter is repeated , if

4

letters are used at a time.

Q. How many words can be made from the letters of the word MONDAY assuming that no letter is repeated if all letters are used but first is a vowel ?

How many words, with or without meaning, can be made from the letters of the word MONDAY, assuming that no letter is repeated if:

(i) 4 letters are used at a time?

(ii) all letters are used at a time?

(iii) all letters are used but first letter is a vowel?

Q. How many words, with or without meaning can be made from the letters of the word

M O N D A Y

, assuming that no letter is repeated, if.
(i)

4

letters are used at a time.(ii) all letters are used at a time(iii) all letters are used but first letter is a vowel?

How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time?
(ii) all letters are used at a time?
(iii) all letters are used but first is vowel?

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How many words can be made from the letters of the word MONDAY assuming that no letter is repeated if 4 letters are used at a time

Total no of letters =6No of letters used at a time =4No of ways =6C46!4!2!=6×5×4!4!×2=15No of ways of using 4 letters =4!=4×3×2=24The total no of ways =15×24=360

How many words can be made from the letters of the word $M O N D A Y$ assuming that no letter is repeated if $4$ letters are used at a time

Total no of letters $= 6$

No of letters used at a time $= 4$

No of ways $=^{6} C_{4}$

$\frac{6!}{4! 2!} = \frac{6 \times 5 \times 4!}{4! \times 2} = 15$

No of ways of using $4$ letters $= 4! = 4 \times 3 \times 2 = 24$

The total no of ways $= 15 \times 24 = 360$