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Q:

In how many ways can 100 soldiers be divided into 4 squads of 10,20, 30, 40 respectively?

A) 1700 B) 18!
C) 190 D) None of these

Answer:   D) None of these

Explanation:

\inline ^{100}\textrm{C}_{10}\times ^{90}\textrm{C}_{20}\times ^{70}\textrm{C}_{30}\times ^{40}\textrm{C}_{40}=\frac{100!}{10!\times 20!\times 30!\times 40!}

Q:

Using numbers from 0 to 9 the number of 5 digit telephone numbers that can be formed is

A) 1,00,000 B) 59,049
C) 3439 D) 6561
 
Answer & Explanation Answer: C) 3439

Explanation:

The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number  of times.

 This can be done in  ways, but '0' is there

So, the numbers starting with '0' are to be excluded which one  in number.

 Total 5 digit telephone numbers =  = 3439

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1 433
Q:

In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends?

A) 240 B) 72
C) 48 D) 36
 
Answer & Explanation Answer: C) 48

Explanation:

DESIGN = 6 letters

No consonants appears at either of the two ends.

=  2 x 4 x 3 x 2 x 1

=  48

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Q:

In How many ways can the letters of the word 'CAPITAL' be arranged in such a way that all the vowels always come together?

A) 360 B) 720
C) 120 D) 840
 
Answer & Explanation Answer: A) 360

Explanation:

CAPITAL = 7

Vowels = 3 (A, I, A)

Consonants = (C, P, T, L)

5 letters which can be arranged in 

Vowels A,I = 

No.of arrangements = =360

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0 311
Q:

The number of ways that 8 beads of different colours be strung as a necklace is 

A) 2520 B) 2880
C) 4320 D) 5040
 
Answer & Explanation Answer: A) 2520

Explanation:

The number of ways of arranging n beads in a necklace is  (since n = 8)

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5 554
Q:

The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is 

A) 7! x 7! B) 7! x 6!
C) 6! x 6! D) 7! x 5!
 
Answer & Explanation Answer: B) 7! x 6!

Explanation:

The students should sit in between two teachers. There are 7 gaps in betweeen teachers when they sit in a round table. This can be done in  ways. 7 teachers can sit in (7-1)! ways.

 Required no.of ways in  = 

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