4 novels can be selected out of 5 in
ways.
2 biographies can be selected out of 4 in
ways.
Number of ways of arranging novels and biographies =
= 30
After selecting any 6 books (4 novels and 2 biographies) in one of the 30 ways, they can be arranged on the shelf in 6! = 720 ways.
By the Counting Principle, the total number of arrangements = 30 x 720 = 21600
There are 7 letters in the word ?Bengali of these 3 are vowels and 4 consonants.
Considering vowels a, e, i as one letter, we can arrange 4+1 letters in 5! ways in each of which vowels are together. These 3 vowels can be arranged among themselves in 3! ways.
Total number of words = 5! x 3!= 120 x 6 = 720
CAPITAL = 7
Vowels = 3 (A, I, A)
Consonants = (C, P, T, L)
5 letters which can be arranged in
Vowels A,I =
No.of arrangements = 5! x =360
As A1 speaks always after A2, they can speak only in 1st to 9th places and
A2 can speak in 2nd to 10 the places only when A1 speaks in 1st place
A2 can speak in 9 places the remaining
A3, A4, A5,...A10 has no restriction. So, they can speak in 9.8! ways. i.e
when A2 speaks in the first place, the number of ways they can speak is 9.8!.
When A2 speaks in second place, the number of ways they can speak is 8.8!.
When A2 speaks in third place, the number of ways they can speak is 7.8!. When A2 speaks in the ninth place, the number of ways they can speak is 1.8!
Therefore,Total Number of ways they can speak = (9+8+7+6+5+4+3+2+1) 8! = = 10!/2
7 × 5 = 35
35 ? 1 = 34
Total number of balls = 2 + 3 + 4 = 9
Total number of ways 3 balls can be drawn from 9 = 9C3
No green ball is drawn = 9 - 3 = 6 = 6C3
Required number of ways if atleast one green ball is to be included = Total number of ways - No green ball is drawn
= 9C3 - 6C3
= 9x8x7/3x2 - 6x5x4/3x2
= 84 - 20
= 64 ways.
H L C N T A U I O
L N A I
There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.
If all the consonants are together then the numberof arrangements = x 1/2! .
But the 7 consonants can be arranged themselves in x 1/2! ways.
Hence the required number of ways = = 1587600
Number of non - negative integral solutions = = 253
Required number of signals =
= 5 + 20 + 60 + 120 + 120 = 325
The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.
Methods for selecting 4 questions out of 5 in the first section = 5 x 4 x 3 x 2 x 1/4 x 3 x 2 x 1 = 5. Similarly for other 2 sections also i.e 5 and 5
So total methods = 5 x 5 x 5 = 125.
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