The number of ways in which four letters of t | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(d) Word $&lsquo;MATHEMATICS$&rsquo; has $2M, 2T, 2A, H, E, I, C, S.$ Therefore $4$ letters can be chosen in the following ways.

Case $I : 2$ alike

Vedclass · Accepted Answer

$2454$

Vedclass · Answer

(d) Word $&lsquo;MATHEMATICS$&rsquo; has $2M, 2T, 2A, H, E, I, C, S.$ Therefore $4$ letters can be chosen in the following ways.

Case $I : 2$ alike of one kind and $2 $ alike of second kind

$i.e.$,$^3{C_2} \Rightarrow $ No. of words ${ = ^3}{C_2}\frac{{4\;!}}{{2\;!\;2\;!}} = 18$
Case $ II$ : $2$ alike of one kind and $2$ different

i.e.,$^3{C_1}{ 	imes ^7}{C_2} \Rightarrow $No.of words ${ = ^3}{C_1}{ 	imes ^7}{C_2} 	imes \frac{{4\;!}}{{2\;!}} = 756$

Case $III$ : All are different

$i.e.$,$^8{C_4} \Rightarrow $No. of words ${ = ^8}{C_4} 	imes 4\;! = 1680$.

Hence total number of words are $2454$.

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

Similar Questions

If $a, b$ and $c$ are the greatest value of $^{19} \mathrm{C}_{\mathrm{p}},^{20} \mathrm{C}_{\mathrm{q}}$ and $^{21 }\mathrm{C}_{\mathrm{r}}$ respectively, then

How many chords can be drawn through $21$ points on a circle?

If $^n{C_r} = {\,^n}{C_{r - 1}}$ and $^n{P_r}{ = ^n}{P_{r + 1}}$, then the value of $n$ is

In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is

A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to