Question

How many words are formed using the letter's of word
"NETWORK"

Answer 1

‘NETWORK’

No. of $2$ letters words ${\Rightarrow }^7{C}_2\times 2!\Rightarrow \frac{7\times 6}{2}\times 2\Rightarrow 42$

No. of $3$ letters words ${\Rightarrow }^7{C}_3\times 3!\Rightarrow \frac{7\times 6\times 5}{3\times 2\times 1}\times 3!\Rightarrow 210$

No. of $4$ letters words ${\Rightarrow }^7{C}_4\times 4!\Rightarrow 7\times 6\times 5\times 4\Rightarrow 840$

No. of $5$ letters words ${\Rightarrow }^7{C}_5\times 5!\Rightarrow 7\times 6\times 5\times 4\times 3\Rightarrow 2520$

No. of $6$ letters words $\Rightarrow 7\times 6\times 5\times 4\times 3\times 2\Rightarrow 5040$

No. of $7$ letters words $\Rightarrow 7!\Rightarrow 5040$

$\therefore$ no. of words $=5040+5040+2520+840+210+42$

$Totalno.ofwords=13692$