50+ Permutations-and-combinations Questions

Permutations-and-combinations Questions Set 4:

Quiz Mode

In how many ways can the letters of the word 'HEADER' be arranged?

Solution:

In how many different ways can the letters of the word 'LEAD' be arranged in such a way that the vowels always come together?

Solution:

In an examination, a candidate is required to pass all five different subjects. The number of ways he can fail is:

Solution:

How many numbers can be made with digits 0, 6, 5 which are greater than 0 and less than a million?
(Note : digits can be repeated)

1084

728

488

496

Solution:

How many 3-digit numbers can be formed from the digits 4, 2, 5, 6, 3 and 9, which are divisible by 5 and none of the digits is repeated?

Solution:

There are 5 doors to a lecture room. In how many ways can a student enter the room through a door and leave the room by a different door?

Solution:

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

10080

120960

49800

None of the above

Solution:

In how many different ways can the letters of the word 'RETAIL' be arranged in such a way that the vowels occupy only the odd positions?

None of the above

Solution:

Nine chairs are numbered 1 to 9. Three women and four men wish to occupy one chair each. First the women chose the chairs from amongst the chair marked 1 to 5; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

⁵C₃ × ⁶C₄

⁵C₃ × ⁴C₂

⁵C₂ × ⁴C₃

None of the above

Solution:

An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …., 9 such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upsidedown-for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?

Permutations-and-combinations Questions Set 4:

In how many ways can the letters of the word 'HEADER' be arranged?

Solution:

In how many different ways can the letters of the word 'LEAD' be arranged in such a way that the vowels always come together?

Solution:

In an examination, a candidate is required to pass all five different subjects. The number of ways he can fail is:

Solution:

How many numbers can be made with digits 0, 6, 5 which are greater than 0 and less than a million?
(Note : digits can be repeated)

Solution:

How many 3-digit numbers can be formed from the digits 4, 2, 5, 6, 3 and 9, which are divisible by 5 and none of the digits is repeated?

Solution:

There are 5 doors to a lecture room. In how many ways can a student enter the room through a door and leave the room by a different door?

Solution:

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

Solution:

In how many different ways can the letters of the word 'RETAIL' be arranged in such a way that the vowels occupy only the odd positions?

Solution:

Nine chairs are numbered 1 to 9. Three women and four men wish to occupy one chair each. First the women chose the chairs from amongst the chair marked 1 to 5; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Solution:

Solution:

Related Question Sets:

Related Topics:

Permutations-and-combinations Questions Set 4:

In how many ways can the letters of the word 'HEADER' be arranged?

Solution:

In how many different ways can the letters of the word 'LEAD' be arranged in such a way that the vowels always come together?

Solution:

In an examination, a candidate is required to pass all five different subjects. The number of ways he can fail is:

Solution:

How many numbers can be made with digits 0, 6, 5 which are greater than 0 and less than a million?(Note : digits can be repeated)

Solution:

How many 3-digit numbers can be formed from the digits 4, 2, 5, 6, 3 and 9, which are divisible by 5 and none of the digits is repeated?

Solution:

There are 5 doors to a lecture room. In how many ways can a student enter the room through a door and leave the room by a different door?

Solution:

In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

Solution:

In how many different ways can the letters of the word 'RETAIL' be arranged in such a way that the vowels occupy only the odd positions?

Solution:

Nine chairs are numbered 1 to 9. Three women and four men wish to occupy one chair each. First the women chose the chairs from amongst the chair marked 1 to 5; and then the men select the chairs from amongst the remaining. The number of possible arrangements is

Solution:

Solution:

Related Question Sets:

Related Topics:

How many numbers can be made with digits 0, 6, 5 which are greater than 0 and less than a million?
(Note : digits can be repeated)