CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A five letter word is to be formed by using the letters of word MATHEMATICS such that
(i) odd places of the word are to be filled with unrepresented letters and
(ii) even places are to be filled with repeated letters.
Then the number of words thus formed is:


A
300
loader
B
360
loader
C
180
loader
D
540
loader

Solution

The correct option is D $$540$$

We have,

Word MATHEMATICS

The letter appearing without repetitions are H,E,C,I and S, so they can be put on odd place.

$$5$$ letters can be placed on $$3$$ places $${{=}^{5}}{{P}_{3}}\,ways$$

On even places positions can be filled by the letter form M,A and T.

Now,

Even places can be filled in two ways.

So, choose one letter from $$3$$ given letters M,A and T and arrange them in $$2!$$ Ways

i.e. $$^{3}{{C}_{2}}\times 2!\,ways.$$

So, the number of ways for even places $${{=}^{3}}{{C}_{1}}{{+}^{3}}{{C}_{2}}\times 2!=9\,\,ways.$$

Hence, the required no. of ways

$$ {{=}^{5}}{{P}_{3}}\times 9 $$

$$ =540\,ways. $$

Hence, this is the answer.


Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image