Advertisements
Advertisements
प्रश्न
Compute:
L.C.M. (6!, 7!, 8!)
Advertisements
उत्तर
LCM of (6!,7! and 8!):
n! = n(n - 1 )!
Therefore, (6!,7! and 8!) can be rewritten as:
8! = 8 X 7 X 6 !
7!= 7 X 6!
6!= 6!
∴ LCM of (6!,7! and 8!) = LCM [8 x 7 x 6!, 7 x 6!] = 8 x 7 x 6 ! = 8!
APPEARS IN
संबंधित प्रश्न
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
Compute:
(i)\[\frac{30!}{28!}\]
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
Twelve students complete in a race. In how many ways first three prizes be given?
In how many ways can six persons be seated in a row?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
12C10
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If 2nC3 : nC2 = 44 : 3, find n.
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
If nC12 = nC8 , then n =
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 80C2
Find the value of 15C4 + 15C5
Find the value of 20C16 – 19C16
If α = mC2, then αC2 is equal to.
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:
| C1 | C2 |
| (a) In how many ways committee: can be formed | (i) 10C2 × 19C3 |
| (b) In how many ways a particular: professor is included | (ii) 10C2 × 19C2 |
| (c) In how many ways a particular: lecturer is included | (iii) 9C1 × 20C3 |
| (d) In how many ways a particular: lecturer is excluded | (iv) 10C2 × 20C3 |
There are ten boys B1, B2, ...., B10 and five girls G1, G2, ...., G5 in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both B1 and B2 together should not be the members of a group is ______.
