Advertisements
Advertisements
प्रश्न
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
उत्तर
Given that P1, P2, P3, ... P10 are 10 persons out of which 5 persons are to be arranged but P1 must occur and P4 and P5 never occur
∴ Selection is to be done only for 10 – 3 = 7 persons
∴ Number of selection = 7C4
= `(7!)/(4!(7 - 4)!)`
= `(7!)/(4!3!)`
= `(7*6*5*4!)/(4!*3*2*1)`
= 35
5 people can be arranged as 5!
So, the number of arrangement = 35 × 5!
= 35 × 120
= 4200
Hence, the required arrangement = 4200.
APPEARS IN
संबंधित प्रश्न
if `1/(6!) + 1/(7!) = x/(8!)`, find x
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
Find r if `""^5P_r = 2^6 P_(r-1)`
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Find x in each of the following:
Which of the following are true:
(2 +3)! = 2! + 3!
In how many ways can 7 letters be posted in 4 letter boxes?
Evaluate each of the following:
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
The number of five-digit telephone numbers having at least one of their digits repeated is
If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
Find the rank of the word ‘CHAT’ in the dictionary.
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
If `""^(("n" – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
