How many different words of 4 letters can be formed from the word Flat earth


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Question Number 178219 by Acem last updated on 14/Oct/22

$H o w m a n y d i f f e r e n t w o r d s o f 4 l e t t e r s c a n$ $b e f o r m e d f r o m t h e w o r d F l a t e a r t h$
Commented by Acem last updated on 14/Oct/22

$I s w e e p i t o v e r t h e p l a n e t$
Commented by Observer last updated on 14/Oct/22

$A r e y o u a f l a t e a r t h e r ?$
	Answered by JDamian last updated on 14/Oct/22

	$I s e e y o u n e e d m u c h h e l p i n M a t h s a s y o u$ $c a n n o t f i n d t w o w o r d s i n F l a t e a r t h .$
	Answered by mr W last updated on 14/Oct/22

	$n u m b e r o f 4 l e t t e r w o r d s f o r m e d$ $f r o m t h e l e t t e r s f l a t e a r t h$ $1) 4 d i f f e r e n t l e t t e r s$ $w o r d s l i k e x y z w w i t h x, y, z, w c h o o s e n$ $f r o m (f, l, a, t, e, r, h) . t o s e l e c t 4 l e t t e r s,$ $t h e r e a r e C_{4}^{7} w a y s . w i t h 4 l e t t e r s w e c a n$ $f o r m 4! w o r d s . t h e r e f o r e w e c a n g e t$ $C_{4}^{7} \times 4! = 840 w o r d s .$ $2) t w o l e t t e r s a$ $w o r d s l i k e a a x y w i t h x, y c h o o s e n$ $f r o m (f, l, t, e, r, h) . t o s e l e c t 2 l e t t e r s,$ $t h e r e a r e C_{2}^{6} w a y s . w i t h 4 l e t t e r s w e$ $c a n f o r m \frac{4!}{2!} w o r d s . t h e r e f o r e w e c a n$ $g e t C_{2}^{6} \times \frac{4!}{2!} = 180 w o r d s .$ $3) t w o l e t t e r s t$ $w o r d s l i k e t t x y .$ $s i m i l a r l y w e c a n g e t$ $C_{2}^{6} \times \frac{4!}{2!} = 180 w o r d s .$ $4) t w o l e t t e r s a a n d t w o l e t t e r s t$ $w o r d s l i k e a a t t . w e c a n g e t$ $\frac{4!}{2! 2!} = 6 w o r d s .$ $t o t a l l y : 840 + 2 \times 180 + 6 = 1206 w o r d s$
	Commented by mr W last updated on 14/Oct/22

	$u s i n g t h e 5 l e t t e r s S Y R I A y o u c a n o n l y$ $f o r m 5 \times 4 \times 3 = 60 w o r d s w i t h 3 l e t t e r s!$ $w o r d s l i k e S S R o r S S S a r e n o t v a l i d,$ $b e c a u s e y o u h a v e o n l y o n e l e t t e r S .$
	Commented by Tawa11 last updated on 14/Oct/22

	$Great sir$
	Commented by Acem last updated on 14/Oct/22
	$Good morning sir! At first, and f.e. if we choose the letters {a, f, t, l} and f.e. again if we formed the word “Flat” and we know that there′s two of both of t, a in this case we will get duplicate words, with this in mind, i made an exception for repeatation and i started with 7 letters to say that the numbers of words are 7^4 = 2401 2nd If i was wrong, please explain to me why 3rd If your solution was correct, please explain the steps 2, 3 and 4 in detail, and of course when you have enough time.$
	$G o o d m o r n i n g s i r!$ $A t f i r s t, a n d f . e . i f w e c h o o s e t h e l e t t e r s {a, f, t, l}$ $a n d f . e . a g a i n i f w e f o r m e d t h e w o r d ‘ ‘ {F l a t}^{″}$ $a n d w e k n o w t h a t {t h e r e}^{'} s t w o o f b o t h o f t, a$ $i n t h i s c a s e w e w i l l g e t d u p l i c a t e w o r d s, w i t h t h i s$ $i n m i n d, i m a d e a n e x c e p t i o n f o r r e p e a t a t i o n$ $a n d i s t a r t e d w i t h 7 l e t t e r s t o s a y t h a t t h e$ $n u m b e r s o f w o r d s a r e 7^{4} = 2401$ $2 n d I f i w a s w r o n g, p l e a s e e x p l a i n t o m e w h y$ $3 r d I f y o u r s o l u t i o n w a s c o r r e c t, p l e a s e e x p l a i n$ $t h e s t e p s 2, 3 a n d 4 i n d e t a i l, a n d o f c o u r s e w h e n$ $y o u h a v e e n o u g h t i m e .$
	Commented by mr W last updated on 14/Oct/22

	$w i t h 7 d i f f e r e n t l e t t e r s y o u c a n o n l y$ $f o r m 7 \times 6 \times 5 \times 4 = 840 w o r d s, n o t$ $7^{4} .$ $w e h a v e o n l y t w o l e t t e r s a a n d t w o$ $l e t t e r s t, t h e r e f o r e w e c a n o n l y u s e$ $t h e s e t w o l e t t e r s t w i c e i n a w o r d .$
	Commented by mr W last updated on 14/Oct/22

	$i h a v e a d d e d s o m e e x p l a n a t i o n i n m y$ $s o l u t i o n a b o v e .$
	Commented by Acem last updated on 14/Oct/22

	$I k n o w t h a t w i t h 7 d i f f . l e t t . w e g e t 840, i m e a n t$ $t o e x c l u d e t h e r e p e t i t i o n o f t, a s o N_{w o r d s} = 7^{4} t o$ $a v o i d g e t t i n g {F l a t}_{f o r e x a m p k e} t h r e e t i m e s$
	Commented by Acem last updated on 14/Oct/22

	$N o t e : I m o d i f i e d t h e q u e s t i o n w i t h$ $‘ ‘ d i f f e r e n t {w o r d s}^{″} b e c a u s e t h e r e i s n o p o i n t$ $i n r e p e a t i n g t h e {r e s u l t s}^{″} T h e r e f o r e t h e s o l u t i o n$ $w i l l c h a n g e t o o .$
	Commented by Acem last updated on 15/Oct/22

	$A c c o r d i n g t o y o u r l o g i c, t h e g r o u p o f t h e a l p h a b e t$ $w o u l d b e u n a b l e t o m a k e w o r d s o f 4 l e t t e r s l i k e :$ $r o o m, w i l l, c i c k, r a r e . . e t c$
	Commented by mr W last updated on 14/Oct/22

	$t o m e ‘ ‘ h o w m a n y {w o r d s}^{″} m e a n s$ $a u t o m a t i c a l l y ‘ ‘ h o w m a n y d i f f e r e n t$ ${w o r d s}^{″} .$
	Commented by Acem last updated on 14/Oct/22

	$G o o d! a b o u t t h i s i a g r e e w i t h y o u . A n d {l e t}^{'} s s t a r t$ $o v e r, t o n a r r o w d o w n t h e {c h o i c e}^{'} s i d e a w i t h a$ $s i m p l e e x a m p l e :$ $I f w e w a n t f o r m w o r d s o f 3 {l e t t e r s}_{s u r e i {d i d n}^{'} t s a y d i f f .}$ $o f t h e w o r d^{″} {S y r i a}^{″} i c a n s a y 5^{3} = 125$ $T i l l n o w i s t h a t o k ? . . . a m w a i t i n g f o r y o u r r e p l a y$
	Commented by Acem last updated on 15/Oct/22

	$B u t h e r e t h e r e p e t i t i o n i s a l l o w e d a s l o n g a s w e$ ${d i d n}^{'} t s a y w o r d s o f 3 d i f f e r e n t l e t t e r s .$ $T h i s i s l i k e w h e n w e d r a w a t h i n g$ $w i t h r e t u r n i n g$
	Commented by mr W last updated on 15/Oct/22

	$w e w a n t t o f o r m t h e w o r d s u s i n g$ $t h e l e t t e r s S Y R I A, w e h a v e o n l y t h e s e$ $5 l e t t e r s t o u s e . t h e w o r d s f o r m e d h a v e$ $a u t o m a t i c a l l y d i f f e r e n t l e t t e r s .$ $w h e n w e w a n t t o f o r m t h e w o r d s u s i n g$ $t h e l e t t e r s f l a t e a r t h, w e h a v e o n l y$ $t h e s e 9 l e t t e r s t o u s e . t h e w o r d s f o r m e d$ $m a y a l s o h a v e s a m e l e t t e r s, f o r$ $e x a m p l e 2 a o r 2 t .$ $i f y o u w a n t t o u n d e r s t a n d o t h e r w i s e,$ $y o u c a n d o .$
	Commented by mr W last updated on 15/Oct/22

	$i {w o n}^{'} t w a s t e m y t i m e a n y m o r e f o r$ $d i s c u s s i n g s u c h n o n - s e n s e s i r .$
	Commented by SLVR last updated on 15/Oct/22

	$n i c e . . . s i r$
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