Question

How many $4$ letter words can be formed from the letters of the word ${}^{\prime }ANSWE{R}^{\prime }$? How many of the words start with a vowel?

Answer 1

$ANSWER$

Case:1 Starts with $A$

$5$ Letters and $3$ Blanks

Number of ways ${=}^5{C}_3=\frac{5\times 4}{2}=10$ Ways

Case: 2 starts with $E$

$5$ Letters and $3$ blanks

Number of ways ${=}^5{C}_3=\frac{5\times 4}{2}=10$ Ways

Hence total ways are $20$