Arrangement with Constraints

Q. Roll numbers are created with a letter followed by 3 digits in it. From the letter A, B, C, D, E and any 3 digits from 0 to 9. Then, in how many possible ways can the roll numbers be generated?
$\left[2\right]$

Q.

Total number of six-digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is

1. $5^6$

2. $\frac{1}{2}·6!$

3. $6!$

4. $\frac{5}{2}(6!)$

Q. How many 4-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 97 and no digit appears more than once?

1. $3024$
2. ${10}^4$
3. ${10}^2$
4. $56$

Q. How many different three letter words, can be made from the letters of the word CHANGE, both with and without meaning but without any repetition?

1. $125$
2. $124$
3. $120$
4. $102$

Q. How many $4$ digits number less than $7000$ can be formed using the digits $0,5,7,1,2,6,8$?

1. $480$
2. $960$
3. $240$
4. $120$

Q. How many $2$ digit even numbers can be formed from the digits $1,4,5,6,9$ if the digits can be repeated?

1. $20$
2. $25$
3. $10$
4. $8$

Q. How many 5 digit numbers can be formed from the digits 0, 1, 3, 7, 9 without repetition which are greater than 40000?

1. $120$
2. $96$
3. $48$
4. None of the above

Q. All the letters of the word $\text{NUMBER}$ are arranged in different possible ways. What are the number of arrangements possible so that no two words are repeated?

1. $6!$
2. $\frac{6!}{6!}$
3. $120$
4. $360$

Q. How many 5 digit numbers can be formed from the digits 0, 1, 3, 7, 9 without repetition which are greater than 40000?

1. $120$
2. $96$
3. $48$
4. None of the above

Q. How many $5$ digit numbers can be formed from the digits $0,1,3,7,9$ without repeatition?

1. $48$
2. $96$
3. $120$
4. $256$

Q. How many $3$ digit numbers can be made using all the even digits between $1$ to $9$?

1. $24$
2. $60$
3. $120$
4. $360$

Q. How many four lettered words can be formed without repetition from the word $\text{FAILURE}$ such that all the words start with the vowels?

1. $24$
2. $840$
3. $480$
4. $60$

Q. Four men have $10$ hats. In how many ways can they wear them?

1. $7!$
2. $6!$
3. $5400$
4. $3040$