ਹੱਲ - Dohrauna bina diyan combian

816

816

ਕਦਮ ਵੇਖੋ

ਕਦਮ-ਬਾ-ਕਦਮ ਸਮਝਾਉਣਾ

1. set vich shabdan di ginti labho

$n$ set vich kul saman da pratinidhitav karda hai:

$c (n, k)$

$c (18, 15)$

$n = 18$

2. set ton chuneya gaya saman di ginti labho

$k$ set ton chuneya gaya saman da pratinidhitav karda hai:

$c (n, k)$

$c (18, 15)$

$k = 15$

3. formula di madad naal sanshayankan (combinations) nu hisab karo

$n$ ( $n$ =18) atey $k$ ( $k$ =15) nu combination formula vich plug karo:
$C (n, k) = \frac{n!}{k! (n - k)!}$

4 ਵਾਧੂ steps

$C (18, 15) = \frac{18!}{15! (18 - 15)!}$

$C (18, 15) = \frac{18!}{15! \cdot 3!}$

$C (18, 15) = \frac{18 \cdot 17 \cdot 16 \cdot 15!}{15! \cdot 3!}$

$C (18, 15) = \frac{18 \cdot 17 \cdot 16}{3!}$

$C (18, 15) = \frac{18 \cdot 17 \cdot 16}{3 \cdot 2 \cdot 1}$

$C (18, 15) = 816$

18 set ton 15 saman chunan de 816 tarike han.

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Combian te permutations

Je tuhanu 2 prakar da crust, 4 prakar de toppings, te 3 prakar di cheese mile, ta tuhanu kinne different pizza combian banan da mauka miluga?
Je race vich 8 swimmers ne, ta 1st, 2nd, and 3rd place winners di kinne different sets ho sakdiyan ne?
Tuhada lottery jittan da ki chance hai?

Ina sawala da jawab mil sakda hai duye sabh to muhke ang da jo probability da hai: combian te permutations. Even though these concepts are very similar, probability theory holds that they have some important differences. Both combian te permutations di madad naal chija di sambhav combian da ginti kita ja sakda hai. Sabh to vadh fark aa ki combian ch order matter nahi karda jiven pizza toppings di combian, te permutations ch order matter karda jiven combination lock da combination set karna, jis nu actually permutation lock keha jaana chahida hai because the order of the input matters.

Ina dova de vich jo common aa, oh hai ki oh saanu sets te ohna de items ya subsets de naal sambandh samjhan vich madad karde ne. Jiven uppar ditian examples vich dikhaya gaya hai, is nu vakhre prakar di situations nu behtar samjhan vich istemal kita ja sakda hai.

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