How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
A
480
B
240
C
360
D
120
Explanation
In the word ''GARDEN'', there are two vowels A and E present, and A should come always before E.
$$\therefore\,\,\,$$ Total no of ways = $${{6!} \over {2!}}$$ = 360
Here A and E has fixed order that is why we divide by 2!.
2
AIEEE 2003
MCQ (Single Correct Answer)
If $${}^n{C_r}$$ denotes the number of combination of n things taken r at a time, then the expression $$\,{}^n{C_{r + 1}} + {}^n{C_{r - 1}} + 2\, \times \,{}^n{C_r}$$ equals
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
A
346
B
140
C
196
D
280
Explanation
Case 1 :
No of ways student can answer 10 questions = $${}^5{C_4} \times {}^8{C_6}$$ = 140
Case 2 :
No of ways student can answer 10 questions = $${}^5{C_5} \times {}^8{C_5}$$ = 56
$$\therefore$$ Total ways = 140 + 56 = 196
4
AIEEE 2003
MCQ (Single Correct Answer)
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
A
$$7!\, \times 5!\,\,$$
B
$$6!\, \times 5!$$
C
$$30!$$
D
$$5!\, \times 4!$$
Explanation
6 men can sit at the round table = $$\left( {6 - 1} \right)! = 5!$$ ways
Now at the round table among 6 men there are 6 empty places and 5 women can sit at those 6 empty positions.
So total no of ways 6 men and 5 women can dine at the round table
= $$5!\, \times {}^6{C_5} \times 5!$$
= $$5!\, \times 6 \times 5!$$
= $$5!\, \times 6!$$
Questions Asked from Permutations and Combinations
On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
