AMDOCS Permutation and Combinations Problems with Solutions Quiz-1

A total team of 6 members needs to be selected which is 11c6 = 462

Now the team head can be selected in 462 X 6 =    2772

For a team 11c5 =462 X 6 = 2772

In the word \\\' ENCYCLOPEDIA \\\', we treat the vowels ‘EOEIA’ as one letter.

Thus, we have NCYCLPD(EOEIA)

Now, we have to arrange 8 letters

Number of ways of arranging these letters= 8! = 40320.

Now, (EOEIA) has 5 letters in which E occurs 2 times and the rest are different.

Number of ways of arranging these letters= 5! / 2!= 60

Required number of words = (40320 x 60) = 2419200.

NTWRKNG (EOI)

So it forms 8 group and R occur twice

8! = 40320

3 vowels can be arranged in 3 ways = 6

Total = 40320 * 6 = 241920

The word RELATION is an 8-letter word, with none of the letters repeating.

The three vowels can be arranged in 3! Ways.

Similarly, the 5 consonants can be arranged in5! Ways.

Hence, the total number of ways = 3! × 5!

By applying the formula   ncr = n!/r!(n-r)!

16!/10!(16-10)!

We get 48048.

There are 8 letters in the word MOUNTAIN of these 4 are vowels and 4 consonants.

There are 4 odd places and 4 even places. 4 vowels can occupy 4 odd places in 4p4 ways and 4 constants can be arranged in 4P4 ways.

Number of words = 4C4+4C3+4C2+4C1= 24

nCr=n!/r!(n-r)!

Section A Section B

A 3 7

B 7 3

So required probability = 10C3 10C7  + 10C7 10C3= 120*120+120*120=28800

The word ('VOWEL' has 5) letters. It has the vowels 'O','E', in it and these two vowels should always come together. Hence, these two vowels can be grouped and considered as a single letter. That is, VWL(OE).

Hence, we can assume total letters as three and all these letters are different.

Number of ways to arrange these three! = 6

All two vowels (OE) are different

Number of ways to arrange these vowels among themselves

=> two! = 2×1 = 2

hence, the required number of ways

2×6=12

Total words are 5 so ways 5! But 2 a are repeating

So 5!/2!=120/2=60

No of ways to choose 3 software engineer out of 12

10C3 = 132