Permutation and combination exercise

1)How many three digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6, (repetition of digits is not allowed
a) 150
b) 100
c) 120
d) None

Explanation:

2) Find the 4-digited numbers can be formed by using digits 1, 2, 4, 6 and 7 that are divisible by 4 (repetition of digits is allowed).
a) 150
b) 175
c) 125
d) None

Explanation:

3) How many numbers can be formed using the digits 2, 3, 5, 6, 7 and 8 that are more than 500 but less than 5000 (repetition of digits is allowed)?
a) 648
b) 540
c) 432
d) 576

Explanation:

4) How many 4-digit numbers can be formed using the digits 0, 1, 2, 4, 5 and 6 that are divisible by 5 (repetition of digits is not allowed)?
a) 118
b) 120
c) 108
d) None

Explanation:

5)How many 3-digit numbers can be formed using the digits 0 to 9 that such that the number do not contain 3 and 6 (repetition of digits is allowed)?
a) 1000
b) 448
c) 512
d) None

Explanation:

6) How many integers, greater than 999 but not greater than 4000, can be formed with the digits, 0, 1, 2, 3, and 4, if repetition of digits is allowed?
a) 499
b) 500
c) 375
d) 376

Explanation:

7)A number lock consists of 4 rings each marked with 10 different numbers. In how many cases the locks cannot be opened?
a) 4 to the power 10
b) 103
c) 10 to the power 4

Explanation:

8) Find the number of 10 digit numbers formed 1, 2, 3, 4 and 8 which are divisible by 4, when repetition is allowed ?
a) 8 * 5 to the power 10
b) 5 to the power 10
c) 8 * 5 to the power 8
d) 7 * 5 to the power 8

Answer:c) 8 * 5 to the power 8

Explanation:

9) In how many ways we can arrange 5 boys and 2 girls, such that girls always sit together?
a) 1500
b) 720
c) 1440
d) None of the above

Explanation:

10) In how many different ways can the letters of the word 'SOFTWARE' be arranged in such a way that the vowels do not come together?
a) 8 !
b) 7 !
c) 8 ! - 3! X 6!
d) None of the above

Answer:c) 8 ! - 3! X 6!

Explanation:

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