मराठी

We Wish to Select 6 Persons from 8, but If the Person a is Chosen, Then B Must Be Chosen. in How Many Ways Can the Selection Be Made? - Mathematics

Advertisements
Advertisements

प्रश्न

We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can the selection be made?

उत्तर

6 people are to be selected from 8.
There are two case.
 (i) When A is selected, then B must be chosen.
∴\[\text{Number of ways} = {}^6 C_4 = 15\]

(ii) When A is not chosen:

\[\text{Number of ways} =^7 C_6 = 7\]

∴ Total number of ways = 15 + 7 = 22

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 17: Combinations - Exercise 17.2 [पृष्ठ १६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 17 Combinations
Exercise 17.2 | Q 23 | पृष्ठ १६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.


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:

(i) exactly 3 girls?

(ii) atleast 3 girls?

(iii) atmost 3 girls?


How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?


Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?


Twelve students complete in a race. In how many ways first three prizes be given?


How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?


From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?


How many three-digit numbers are there?


In how many ways can six persons be seated in a row?


A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.


Evaluate the following:

14C3


Evaluate the following:

n + 1Cn


If 15Cr : 15Cr − 1 = 11 : 5, find r.


If n +2C8 : n − 2P4 = 57 : 16, find n.


In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?


In how many ways can a football team of 11 players be selected from 16 players? How many of these will

include 2 particular players?


From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?


A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?


How many triangles can be obtained by joining 12 points, five of which are collinear?


Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.


A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?


If 20Cr = 20Cr−10, then 18Cr is equal to


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to


Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?


Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3


The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______ 


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.


A convex polygon has 44 diagonals. Find the number of its sides.


The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is ______.


In a football championship, 153 matches were played, Every two teams played one match with each other. The number of teams, participating in the championship 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 ______.


A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.


There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.


There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.


The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.


From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×