Question

In marthematics
( n O cdot ) of ( r A=2 )
no. of ( T=2 )
no. ( A=2 )
ofter luters ( forall, E, I, c, s ) are sinfle letters
alike ond two alik case
( 1-T w_{0} )
We have
3 groups of same luters ( i cdot e cdot 2 M cdot s, 2 T^{prime} s ) ard ( 2 A_{S}^{prime} )
ad we have to sulet two out so this can be dom in ( 3 C_{2} ) two different. here ir this
owt of 7 group ( i cdot f cdotleft(2 text { pes } 27^{circ} ) sent. right.
( 7 c_{2}+3 c_{1} )
( mid cos x-3] ) all diffirent differet letors ( quad M, T, A_{1} H, E, I, C S )
this cun be don in 8 cumay
Arrarginent - for ist con. ( frac{4 !}{2 ! 2 !} ) for ( i^{-d} cos frac{4 !}{2 !} )
dor third con cil. final anw ( -3 c_{2} frac{x q !}{2 ! 2 !}+3 c_{1} times 7 c_{2} times frac{4 !}{2 !}+8 c_{4} times 4 ! )
( 18+756+1680=2454 )

# 53. Find the number of ways in which arrangements of 4 letters can be made from the word "MATHEMATICS. (a) 1,680 (b) 756 (C) 18 (d) 2454

Solution