Commpilation - Permutation and Combinations. (under development)

None of the letter should be correct
D(n)=n![1- (1/1!) +(1/2!) ....(-1)ⁿ 1/n!]

ⁿ⁺¹C_r = ⁿC_r + ⁿC_r-1

ⁿP_r = r.^n-1P_r-1 + ^n-1P_r

Total number of ways in which a selection can be made:-
[({p+1}{q+1}{r+1}....)-1]

Positive Integral Solution
a+b+c=10
⁹C₂

Non negative integral solution
^s+n-1C_n-1

(n-1)!*(sum of n digits)*(11111... n times)

There are 26 alphabets in english language.
There are 52 playing cards.
Fibonnaci series plus 1, no two adjacent adjacentbox contain blue ball


12 book among 3 boys 12!/(3!)^3

12 book in three parcels 12!/(3!)^3.3!

LOD1

Can anyone explain how to find number of distinct terms in the expansion of (a+b+c)^20?

a. 231
b. 253
c. 242
d. 210
e. 228

Solution
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In how many ways can 4 prizes each having 1st,2nd and 3rd positions be given to 3 boys ,if each boy is eligible to receive more than one prize?

1.12P3

2. 6^4

3. 4^3

4.12C4 * 3!

5.3^12

Solution

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In how many ways can the crew of a 10 oared bot be arranged, when of the 10 persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?

(a) 10! / 2!3! (b) 10! / 8!7! (c) 5! / 3!2! (d) (5!)3/ 3!2!

Solution
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A double decked bus can accomodate 110 passengers,50 in the upper deck and 60 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck?

1. 85!50!60!/40!45!
2. 85!/40!45!
3. 110!/50!60!
4. 110!50!60!/40!45!
5. 110!/40!45!

Solution
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how many way could 15 different books be divided in 3 boys

Solution
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Twelve friends go out for a dinner to a restaraunt where they find two circular tables, one with 7 chairs and the other with 5 chairs. In how many ways can the group settle down themselves for dinner?

(a) 12! (b) 12 ! / 7!5! (c) 12! / 35 (d) 12!5!7!

Solution
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Find the number of selections that can be made taking 4 letters from the word "ENTRANCE". 

A.70 

B.36 

C. 35 

D.72 

OA B 

2. In the above word , the number of arrangements using the 4 letters. 

OA. 606

Solution

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There are 5 copies of a Math book, 4 copies of a Physics book, and 3 copies of a Chemistry book. The number of ways in which one or more books can be given away is:
(a) 89 (b) 119 (c) 60 (d) 59

Solution

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In how many ways can 4 couples be seated around a circular table such that people of the same gender do not sit in the adjacent positions and exactly one of the four couples sit in the adjacent position.

Solution

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Seven boxes numbered 1 to 7 are arranged in a row.Each is to be filled by either a black or blue coloured balls such that no two adjacent boxes contain blue coloured balls.In how many ways can the boxes be filled with the balls?

Solution

LOD2 (Permutation Combinations) >> << Home