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New answer posted
a year agoContributor-Level 10
21. There are 11 letters of which M appears 1 time, I appears 4 times, S appears 4 times and P appears 2 times.
The required number of arrangements =
= 11 * 10 * 9 * 5
= 34650
When the four I occurs together we treat them as single object IIII. This single object together with 7 remaining object will account for 8 object which have 1-M. 2-P and 4-S.
So, required number of permutation =
= 840
Therefore, total no. of permutation in which 4-I's do not come together
= 34650 – 840
= 33810
New answer posted
a year agoContributor-Level 10
20. i. The permutation of 6 letters in MONDAY taken 4 at a time without repetition is
ii. The permutation of 6 letters in MONDAY when all letters are taken at a time is
6P6 = = = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
iii. The permutation of having one of the two vowels (O, A) as first letter from the word MONDAY when all letters are taken at a time is
2P1 = = 2
After fixing one of the vowel as first letter we can rearrange the remaining 5 letters taking 5 at a time
5P5 = = = 5! = 5 * 4 * 3 * 2 * 1 = 120
Therefore, total permutation when all letters are used but first letter is vowel from the word MONDAY = 2
New question posted
a year agoNew question posted
a year agoNew answer posted
a year agoContributor-Level 10
19. Since no letter is repeated in the word EQUATION.
The permutation of 8 letters taken all at a time
= 8P8
=
=
= 8! [since, 0! = 1]
= 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 40320
New answer posted
a year agoContributor-Level 10
15. The permutation of 5 different digits namely 1, 2, 3, 4, 5 taken 4 at a time is
5P4 = = = 5 * 4 * 3 * 2 * 1 = 120
The permutation of having 2 or 4 at ones place is
2P1 = = = 1 * 2 = 2
After fixing one of the even number at last digit we can rearrange the remaining four digits taking 3 at a time. i.e.
4P3 = = = 4 * 3 * 2 * 1 = 24
Therefore, total permutation of 4 digit even number using 1, 2, 3, 4, 5
= 24 * 2
= 48
New answer posted
a year agoContributor-Level 10
14. The permutation of having even number at the last digit from the given 6 different digits namely 1, 2, 3, 4, 5, 6 to form a 3-digit number is
After taking one of the even number as last digit we can rearrange the remaining 5 digits taking 2 at a time. i.e.
Therefore, The required number = 20 * 3 = 60
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