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Permutation and combination

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Please solve:

how many words using all 8 letters of TATHAGAT can be formed such that 
a) no two Ts are together?
b) first letter is not T and last letter is not A?

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 What should be the approach to solve the question in screenshot?

image
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The collection of the questions are really great it will help me for my upcoming exams.

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Find the number of ways to distribute 2n different balls into
(a) n equal lots
(b) equally among n children

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How many numbers are there between 99 and 1000, having at least one of their digits 7?

Neraj (TG) 13/07/2024 4:16 pm
0
image

(a) 36/13  (b) 36/91   (c) 91/36  (d) 13/36

Neraj (TG) 13/07/2024 4:40 pm

@neha-singh 

Probability of getting both are red = 9c2/14c2 = 36/91 

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The number of all possible matrices of order 2×2 with each entry 0 or 1 is :

1.27

2.18

3.16

4.81

Neraj (TG) 13/07/2024 3:51 pm

@neha-singh 

The number of possible entries of 2×2 matrix is 4. Every entry has two choice, 0 or 1.

Thus, the total number of choices is = 2×2×2×2 = 16

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A,B,C,D,E,F,G and H are 8 students in a school. The class teacher wants to send 4 students each for a quiz competition and drawing competition such that each students goes for exactly one competition. Assuring that each student is capable of participating in either of the two competitions, in how many ways can the class teacher create the two teams?

Neraj (TG) 18/08/2024 6:27 pm
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