CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The number of ways in which four letters of the word MATHEMATICS can be arranged is given by:


A
136
loader
B
192
loader
C
1680
loader
D
2454
loader

Solution

The correct option is B $$2454$$
Two pairs of identical letters can be arranged in $$^3C_2\dfrac {4!}{2!2!}$$ ways. 
Two identical letters and two different letter can be arranged in $$^3C_1\times {}^7C_2\times \dfrac {4!}{2!}$$ ways. 
All different letters can be arranged in $${}^8P_4$$ ways.
$$\therefore$$ Total number of arrangements
$$={}^3C_2\dfrac {4!}{2!2!}+{}^3C_1\times {}^7C_2\times \dfrac {4!}{2!}+\dfrac {8!}{4!}=2454$$.

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image