Question

How many four letter words are possible using the first $5$ letters of the alphabet if letters cannot be repeated ?

Answer 1

First write down the elements or letters you have to form the four letter words, then make a table with four boxes and use your imagination in how many ways you can fill the first box with the elements or letters you have, then think for second and similarly for all boxes up to the last one keeping in mind that repetition is of elements is allowed. After finding the possibilities of filling all the boxes, multiply possibilities of filling all the boxes to get the required answer.

Complete step by step answer:
To find how many four letter words are possible using the first $5$ letters of the alphabet if letters cannot be repeated, we will first make a set of elements we have for forming the four letter words.
S = \left\\{ {a,\;b,\;c,\;d,\;e} \right\\}
That is we have five letters.Now making a table of four boxes in a row,

${1^{st}}$	${2^{nd}}$	${3^{rd}}$	${4^{th}}$

Let us think in how many ways we can fill the ${1^{st}}$ box? If we have five elements/letters.Yes, in five ways, similarly if repetition is allowed then we can fill the other boxes too in five ways.Therefore required possible ways $= P1 \times P2 \times P3 \times P4,\;{\text{where}}\;P1,\;P2,\;P3\;{\text{and}}\;P4$ are possibilities for ${1^{st}},{\text{ }}{2^{nd}},{\text{ }}{3^{rd}}{\text{and }}{4^{th}}$ box.

\therefore 625 \\\ $$ **Therefore ${\text{in}}\;625$ ways we can form four letter words with first five alphabets when repetition is allowed.** **Note:** In order to solve this type of questions, reading the conditions carefully is the most important part of solving the question, because when you understand the question as well as its given conditions then at that spot you have already solved it half, rest you have to work with your imagination skills.