20-students-are-numbered-with-the-numbers-from-1-to-20-10-students-are-randomly-selected-what-is-the-probability-that-the-sum-of-their-numbers-is-exactly-100-

Question Number 179699 by mr W last updated on 01/Nov/22

20 s t u d e n t s a r e n u m b e r e d w i t h t h e

n u m b e r s f r o m 1 t o 20 . 10 s t u d e n t s a r e

r a n d o m l y s e l e c t e d . w h a t i s t h e

p r o b a b i l i t y t h a t t h e s u m o f t h e i r

n u m b e r s i s e x a c t l y 100 ?

Commented by Rasheed.Sindhi last updated on 01/Nov/22

∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \cdot \cdot \cdot 100^{'} s & 99 ∣^{'} s

Now {we}^{'} ve to select 9 bars (divisions)

(or {we}^{'} ve to put 9 divisions (bars))

in a particular way which fulfills your

restrictions \dots

I remember this way or some type like

this which was introduced by sir

prakash jain / m r W s i r \dots

perhaps this method helps in such

questions \dots a l t h o u g h I^{'} m n o t s u r e .

Commented by mr W last updated on 01/Nov/22

t h e d i f f i c u l t y i s t h a t t h e s u m o f t h e

10 n u m b e r s s h o u l d b e 100 . w i t h “ s t a r s

a n d {b a r s}^{″} m e t h o d w e c a n n o t t r e a t t h e

s u m o f t h e n u m b e r s .

Commented by JDamian last updated on 01/Nov/22

p = \frac{c o m b i n a t i o n s s u m i n g u p 100}{a l l c o m b i n a t i o n s} ?

Commented by mr W last updated on 01/Nov/22

t h i s q u e s t i o n i s s i m i l a r t o Q 179420 .

b u t d u e t o t h e l a r g e n u m b e r 100, w e

c a n n o t e n u m e r a t e a l l c o m b i n a t i o n s

w h i c h g i v e t h e s u m 100 .

Commented by Rasheed.Sindhi last updated on 01/Nov/22

S i r i f w e p u t 9 b a r s b e t w e e n 100 s t a r s

t h e n w i l l t h e s u m o f t e n g r o u p s (m a d e

b y b a r s) n o t b e 100 ?

E x e c u s e m e i f I n o t g e t t o y o u .

Commented by mr W last updated on 01/Nov/22

t h i s i s t r u e . b u t h o w c a n y o u r e l a t e

t h e 100 s t a r s t o t h e n u m b e r s f r o m 1

t o 20 ?

a c t u a l l y w e j u s t w a n t t o d e t e r m i n e

h o w m a n y s o l u t i o n s f o l l o w i n g i n t e g e r

e q u a t i o n h a s :

n_{1} + n_{2} + \dots + n_{10} = 100

w i t h 1 ⩽ n_{1} < n_{2} < \dots < n_{10} ⩽ 20

Commented by Rasheed.Sindhi last updated on 01/Nov/22

Y e s s i r {y o u}^{'} r e r i g h t!

Commented by mr W last updated on 01/Nov/22

u s i n g g e n e r a t i n g f u n c t i o n w e f i n d o u t

5095 w a y s t o s e l e c t 10 n u m b e r s w h o s e

s u m i s 100 . s o t h e p r o b a b i l i t y i s

p = \frac{5095}{C_{10}^{20}} = \frac{5095}{184756} \approx 2 . 76 %

Commented by mr W last updated on 01/Nov/22

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