Question

How many words can be made form the letters of the word MONDAY, assuming that no letter
is repeated if,
i) 2 letters are used at a time.
(ii) 4 letters are used at a time.​

Answer 1

Answer:

$\bigstar{\bold{Number\:of\:words\:formed\:if\:2\:letters\:are\:used=30}}$

$\bigstar{\bold{Number\:of\:words\:formed\:if\:4\:letters\:are\:used=360}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• The word MONDAY

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Words that can be formed if 2 letters are used at a time
• Word that can be formed if 4 letters are used at a time

$\Large{\underline{\underline{\bf{Solution:}}}}$

If 2 letters are used at a time:

➔ We have to find out number of words formed with two letters

➔ The total number of letters in the word MONDAY = 6

➔ Number of letters used = 2

➔ Hence,

     $\sf{Number\:of\:words\:that\:can\:be\:formed=^{6}P_2}$

     $\sf{Number\:of\:words\:that\:can\:be\:formed=\dfrac{6!}{(6-2)!} }$

     $\sf{Number\:of\:words\:that\:can\:be\:formed=\dfrac{6!}{4!} }$

     $\sf{Number\:of\:words\:that\:can\:be\:formed=\dfrac{6\times 5\times 4!}{4!} }$

    Number of words that can be formed = 6 × 5

    Number of words that can be formed = 30

   

    $\boxed{\bold{Number\:of\:words\:formed\:if\:2\:letters\:are\:used=30}}$

If 4 letters are used at a time:

➔ Now we have to find the number of word that can be formed if 4 letters are used at a time.

➔ Total letters in MONDAY = 6

➔ Number of letters used = 4

➔ Hence,

    $\sf{Number\:of\:words\:that\:can\:be\:formed=^{6}P_4}$

    $\sf{Number\:of\:words\:that\:can\:be\:formed=\dfrac{6!}{(6-4)!} }$

    $\sf{Number\:of\:words\:that\:can\:be\:formed=\dfrac{6!}{2!} }$

    $\sf{Number\:of\:words\:that\:can\:be\:formed=\dfrac{6\times 5\times 4\times 3\times 2!}{2!} }$

    Number of word that can be formed = 6 × 5 × 4 × 3

    Number of words that can be formed = 30 × 12

    Number of words that can be formed = 360

   

   $\boxed{\bold{Number\:of\:words\:formed\:if\:4\:letters\:are\:used=360}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

$\sf{^{n} P_r=\dfrac{n!}{(r-n)!} }$

$\sf{^{n} C_r=\dfrac{n!}{r!\times (r-n)!} }$