Wiley Edge Permutations and Combination Quiz-1

Explanation:
Total Number of letters = 6
Number of time P appears = 2
Therefore Number of permutations = 6! / 2!
=> 720 / 2
=> 360

Explanation:

Since each character in the password can be either a lowercase letter (26 options) or a digit (10 options)

The total number of password combinations can be calculated by multiplying the number of options for each character: 36x 36 x 36 x 36 =</span><span style="font-weight: 400;"> 36^4</span><span style="font-weight: 400;"> = 16,79,616

Explanation:
Total Number of letters = 4
Number of times A appears = 2
Therefore Number of permutations = 4! / 2!
=> 24 / 2
=> 12

Explanation:
The number of different combinations of toppings can be calculated using the combination formula:
C(8, 3) = 8! / (3! * (8-3)!) = 56

Explanation:
Total Number of letters = 8
Number of times I appears = 2
Number of times N appears = 2
Therefore Number of permutations = 8! /(2! * 2!)
=> 40320 / 4
=> 10080

Explanation:
The number of different combinations of colors can be calculated by selecting 2 balls from a group of 10 (5 red, 3 blue, and 2 green), which can be calculated using the combination formula: C(10, 2)
=> 10! / (2! * (10-2)!)
=> 45.

Explanation:
Total Number of letters = 6
Therefore Number of permutations = 6!
=> 720

Explanation:
The number of different pairs that can be formed is given by selecting 2 students from a group of 10, which can be calculated using the combination formula: C(10, 2)
=> 10! / (2! * (10-2)!)
=> 45

Explanation:
Total Number of letters = 5
Number of times A appears = 2
Number of times R appears = 2
Therefore Number of permutations = 5!/(2!*2!)
=> 120/4
=> 30

Explanation:
Identify the vowels and consonants in the word: Vowels: O, I, O, U Consonants: C, N, S, T, T, T, N
Arrange the consonants in alphabetical order: C, N, N, S, T, T, T
Place the vowels in the spaces between the consonants: C, N, N, S, T, T, T There are 8 spaces between the consonants (including the ends), where we can place the vowels.
Choose 4 spaces out of the 8 spaces to place the vowels: We can select 4 spaces out of 8 using combinations: C(8, 4) = 70.
Number of ways to arrange vowels = 4!/2! = 6
Total number of arrangements: C(8, 4) * 6 = 420