Permutation with given condition

Diagram above shows 5 letter and 3 digits.

A code is to be formed using those letters and digits. The code must consist of 3 letters followed by 2 digits. 

How many codes can be formed if no letter or digit is repeated in each code ?

• $3P1\times5P1$

• $3P3\times2P2$

• $5P3\times3P2$

• $5P5\times3P3$

Diagram above shows five cards of different letters.

Find the number of these arrangements in which the letters E and A are side by side .

• $3P3\times2P2$

• $4P4\times2P2$

• $4P3\times3P2$

• $5P2\times3P3$

Diagram above shows seven letters cards.

A four-letter code is to be formed using four of these cards.

Find the number of different four letter codes which end with a consonant.

• $3P3\times4P1$

• $6P3\times4P1$

• $7P4$

• $7P3\times4P1$

A group of 6 boys and 3 girls want to take a group photograph.
Find the number of ways that the group member can be arranged in a row, if the three girls sit next to each other.

•  $3P3\times7P7$  

•  $3P3\times6P6$  

•  $3P3\times7P7\times2P2$  

•  $3P3\times6P6\times2P2$  

Diagram above shows six numbered cards.

A four-digit number is to be formed by using four of these cards.

How many different odd numbers can be formed?

• $3P1\times5P3$

• $3P1\times5P5$

• $4P1\times5P3$

• $4P1\times5P5$

There are 4 different Science books and 3 different mathematics books on a shelf.

Calculate the number of different ways to arrange all the books in a row if all the Mathematics books are next to each other.

• $3P3\times4P4$

• $3P3\times5P5$

• $2P2\times5P2$

• $2P2\times5P5$

Diagram above shows seven letter cards.

A code of five letter are formed from the cards.

Find the number of code can be form where the code begins with a vowel and end with a consonant.

• $2P1\times5P1\times5P5$

• $2P1\times5P1\times5P4$

• $2P1\times5P1\times5P3$

• $2P1\times5P1\times5P2$

Diagram above shows seven letters cards.

How many ways can the letter be arranged to form a 5 letters code?

• $5P5$

• $7P5$

• $7P7$

• $7P3$

Diagram above shows five letter cards. How many way can all the letter cards be arranged in a row if all the vowel must be separated?

• $2P2\times3P3$

• $3P3\times3P3$

• $3P3\times4P2$

• $3P3\times4P4$

Diagram above shows seven letter cards.

How many way can all the letter cards be arranged in a row if all the vowel must be separated?

• $3P3\times4P4$

• $4P4\times5P3$

• $4P4\times5P5$

• $4P4\times7P7$