Question

Find the number of 2 lettered words, with or without meaning, that can be formed out of the letters of the word TIME, where the repetitions of the letters (a) is not allowed (b) is allowed.

Answer 1

Answer:

(a) 12

(b) 16

Step-by-step explanation:

Hi,

To find the number of 2 lettered words that can be

formed out of the letters of the word TIME

(a) If repetitions of letters are not allowed,

2 letters which form the word can be chosen in ⁴C₂ = 6 ways

These chosen letters can be permuted among themselves

in 2 different ways.

Hence, total number of words that can be formed are

6*2 = 12(Since, it includes selection of 2 letters AND arrangement

of 2 selected letters).

Hope, it helps !

(b)If repetition is allowed

First letter of the 2 letter word can be selected in 4 different ways,

Similarly even second letter can be selected in 4 different ways,

hence selection of  first letter of the word AND selection of second

letter of word can be done in 4*4 = 16 ways.( here, we need not

multiply by 2 since, the way we are selecting is automatically fixing

the position/arrangement)

Hope, it helps

Answer 2

Answer:

we need to fill two places we have 4 letters

so when repitetion not allowed first place can be filled with 4 ways (any among the 4 no.) the second place by any of the 3 nos hence 3 ways

so total ways 4 times 3 is 12

now when repitetion allowed first place 4 ways

second place again 4 ways as the no in the first place can be repeated in the second place so there are again 4 ways to fill the second place ie the remaining 3 letters and the letter itself in the first place hence 4 ways soo final answer is 4 times 4 that's 16

so when repitetion allowed 16

when not its 12....

LETS HELP EACHOTHER BROTHER......