Total number of distinct 4 letters words that can be formed from the letters of the word 'NANDINI'. so that at most 2 alike letters are together, is -

Question

Total number of distinct 4 letters words that can be formed from the letters of the word 'NANDINI'. so that at most 2 alike letters are together, is - (A) 104 (B) 106 (C) 108 (D) 114

Tardigrade Admin · Accepted Answer

3 alike and 1 distinct arrow 1 C 1 × 3 C 1 ×[(4 !/3 !)-2 !]=6 2 alike 2 distinct arrow 2 C 2 ×((4 !/2 ! 2 !))=6 2 alike and 2 distinct arrow 2 C 1 × 3 C 2 × (4 !/2 !)=72 4 distinct arrow 4 !

Q. Total number of distinct 4 letters words that can be formed from the letters of the word 'NANDINI'. so that at most 2 alike letters are together, is -

104

106

108

114

$3$ alike and $1$ distinct $\to^{1} C_{1} \times^{3} C_{1} \times [\frac{4 !}{3 !} - 2!] = 6$
$2$ alike $2$ distinct $\to^{2} C_{2} \times (\frac{4 !}{2 ! 2 !}) = 6$
$2$ alike and $2$ distinct $\to^{2} C_{1} \times^{3} C_{2} \times \frac{4 !}{2 !} = 72$
4 distinct $\to 4!$

Q. Total number of distinct 4 letters words that can be formed from the letters of the word 'NANDINI'. so that at most 2 alike letters are together, is -

104

106

108

114

3 alike and 1 distinct →1C1​×3C1​×[3!4!​−2!]=6 2 alike 2 distinct →2C2​×(2!2!4!​)=6 2 alike and 2 distinct →2C1​×3C2​×2!4!​=72 4 distinct →4!

$3$ alike and $1$ distinct $\to^{1} C_{1} \times^{3} C_{1} \times [\frac{4 !}{3 !} - 2!] = 6$
$2$ alike $2$ distinct $\to^{2} C_{2} \times (\frac{4 !}{2 ! 2 !}) = 6$
$2$ alike and $2$ distinct $\to^{2} C_{1} \times^{3} C_{2} \times \frac{4 !}{2 !} = 72$
4 distinct $\to 4!$