Advertisements
Advertisements
प्रश्न
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
पर्याय
12
24
18
none of these.
Advertisements
उत्तर
12
All S's can be placed either at even places or at odd places, i.e. in 2 ways.
The remaining letters can be placed at the remaining places in 3!, i.e. in 6 ways.
∴ Total number of ways = 6 x 2 = 12
APPEARS IN
संबंधित प्रश्न
Evaluate 4! – 3!
Is 3! + 4! = 7!?
Compute `(8!)/(6! xx 2!)`
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Which of the following are true:
(2 × 3)! = 2! × 3!
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Evaluate each of the following:
Evaluate each of the following:
P(6, 4)
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, 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
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
If (n+2)! = 60[(n–1)!], find n
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
If nP4 = 12(nP2), find n.
Evaluate the following.
`(3! + 1!)/(2^2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
The number of ways to arrange the letters of the word “CHEESE”:
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
How many ways can the product a2 b3 c4 be expressed without exponents?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
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! |
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
