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

Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is

Determine the number of $5 -$ card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.

The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is

There are two urns. Urm $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urm two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

How many numbers greater than $1000000$ can be formed by using the digits $1,2,0,2,4,2,4 ?$