Permutations and Combinations

8. L.H.S = 3! + 4!

= (1 * 2 * 3) + (1 * 2 * 3 * 4)

= 6 + 24

= 30

R.H.S = 7!

= 1 * 2 * 3 * 4 * 5 * 6 * 7

= 5040

As, L.H.S ≠ R.H.S

3! + 4! ≠ 7!

1. We know that, n! = n (n – 1) (n – 2)…….

i. 8!

8! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8

= 40320

ii. 4! – 3!

= (1 * 2 * 3 * 4) – (1 * 2 * 3)

= 24 – 6

= 18

6. To generate a signal which requires 2 flags one below another we can have the following combination of any of the 5 flag at top and the one of the remaining 4 flag at the bottom.

Hence, total no. of possible combination = 5 * 4 = 20

5. When a coin is tossed one time a head or a tail is the possible outcome.

So, when a coin is tossed 3 times the total number of possible outcomes = 2 * 2 * 2 = 8

4. For the 5-digit telephone number that can be constructed using 0 to 9 if each number starts with 67 and no digit appears more than once we can have

So total number of possible combination = 1 * 1 * 6 * 7 * 8 = 336

3. To form a 4-letter code using the first 10 letters of the English alphabet without repeating we can have 10, 9, 8 and 7 numbers of letters to be filled at ones, tens, hundreds and thousands place simultaneously.

Hence, total no. of 4-letter code that can be made using the first 10-letter of English alphabet = 7 * 8 * 9 * 10 = 5040

2. Since we are given with six numbers (1, 2, 3, 4, 5, 6) to form 3-digit even number and also repetition is allowed.

We can have only the number 2, 4, 6 in the ones place and all the six numbers can fill the tens and hundreds place.

So, total number of 3-digit even number that can be formed by 1, 2, 3, 4, 5, 6

= 6 * 6 * 3

= 108

1. i. Since repetition of number is allowed and there are five numbers which can be used to form the necessary 3-digit numbers we can have five numbers that can fill the ones, tens and hundreds place.

So, total number of possible 3-digit number = 5 * 5 * 5 = 125

ii. Since repetition of number is not allowed. There are total 5 numbers which can fill the ones places then 4 and 3 numbers which can fill the tens and hundreds place simultaneously.

So, total number of possible 3-digit number = 3 * 4 * 5 = 60