How many arrangements of the word TRIGONAL can be made if only two vowels and th

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Question
How many arrangements of the word TRIGONAL can be made if only two vowels and three consonants are used?
Options
A. 6300
B. 3600
C. 6400
D. 7200

Correct Answer

3600

Explanation

First we need to choose two vowels $3 C_{2}$ and then three consonants $5 C_{3}$ . Now that we have 5 letters required to make the word,arrange them in 5! ways.

So, $3 C_{2} * 5 C_{3} * 5! = 3600$

Permutation and Combination problems

Search Results

1. A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls.How many councils can have Jason on the council?
Options
A. 715
B. 725
C. 419
D. 341

2. From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?
Options
A. 103336
B. 120000
C. 108336
D. 108333

3. There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference. If the members of the club decide to send two juniors and two seniors, how many different groupings are possible ?
Options
A. 23024
B. 24023
C. 23023
D. 25690

4. In how many ways can the letters of the word "PROBLEM" be rearranged to make 7 letter words such that none of the letters repeat?
Options
A. 49
B. 7!
C. 7^7
D. 7^3

5. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
Options
A. 4!/2!
B. 3!/2!
C. (4! x 3!) / 2!
D. 36

6. A research team of 6 people is to be formed from 10 chemists,5 politicians, 8 economists and 15 biologists.How many teams have atleast 5 chemists?
Options
A. 7350
B. 6400
C. 6379
D. 7266

7. There are 7 men and 10 women on a committee selection pool.A committee consisting of President,Vice-President, and Treasurer is to be formed.How many ways can exactly two men be on the committe ?
Options
A. 1200
B. 1240
C. 1260
D. 1620

8. If each of the 8 teams in a league must play each other three times,how many games will be played?
Options
A. 72
B. 84
C. 36
D. 79

9. In how many different ways can five persons stand in a line for a group photograph?
Options
A. 120
B. 240
C. 360
D. 720

10. First,second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered.In how many different ways can the prizes be awarded?
Options
A. 1736
B. 1716
C. 1216
D. 1346

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