Question

letters of word MATHEMATICS are arranged at random. Probability that word formed contains the word MATHS

Answer 1

Prabability that word formed contains the word MATHS is $\frac{1}{120}$.

Step-by-step explanation:

We know that there are 11 letters in word 'MATHEMATICS' in which there are 2 'M', 2 'A' and 2 'T'. Prabability 'P' of word contains 'MATHS' by arranging (selection) of word 'MATHEMATICS' is:

We know,

                                ⇒ P = $\frac{Favourable conditions}{Total conditions}$

                Using combination, The fovarable conditions are,

                                        =      $^{11}C_5\times \frac{6!}{2!\times2!\times2!}$

                                           ⇒ $^{11}C_5$ =  $\frac{11!}{6!\times5!}$

  Now, Total consitions are,      

                                          = $\frac{11!}{2!\times2!\times2!}$

According to Formula of probability,

                                            ⇒ P =    $\frac{Favourable conditions}{Total conditions}$

                                            ⇒ P =   $\frac{^{11}C_5\times \frac{6!}{2!\times2!\times2!}}{\frac{11!}{2!\times2!\times2!}}$

After solving the above equation , we get the prbability which is,

                     

                                             ⇒ P = $\frac{1}{120}$