(D) Each of the first $3$ questions can be answered in $4$ ways.Each of the last $3$ questions can be answered in $5$ ways.By the fundamental principl

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) Each of the first $3$ questions can be answered in $4$ ways.Each of the last $3$ questions can be answered in $5$ ways.By the fundamental principle of counting,the total number of possible sequences of answers is the product of the number of choices for each question.Total sequences $= 4 \times 4 \times 4 \times 5 \times 5 \times 5$Total sequences $= 4^3 \times 5^3 = 64 \times 125 = 8000$.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

Easy

There are $6$ multiple choice questions on an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next $3$ have $5$ each?

A
$6000$
B
$5000$
C
$4000$
D
$8000$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Permutation and Combination

Subtopic

Permutation and Combination

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

Medium

View Solution

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

Difficult

View Solution

The number of $7$-digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is:

Easy

View Solution

In how many ways can $10$ people line up at a ticket window of a cinema hall?

Medium

View Solution

$3$ boys $B_1, B_2, B_3$ and $6$ girls $G_1, G_2, . . . , G_6$ are to be seated in a row. The number of ways they can be seated such that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to:

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

There are $6$ multiple choice questions on an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next $3$ have $5$ each?

Similar Questions

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

If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman,then the number of seating arrangements is

The number of $7$-digit numbers which can be formed using the digits $1, 2, 3, 2, 3, 3, 4$ is:

In how many ways can $10$ people line up at a ticket window of a cinema hall?

$3$ boys $B_1, B_2, B_3$ and $6$ girls $G_1, G_2, . . . , G_6$ are to be seated in a row. The number of ways they can be seated such that $B_1, B_2$ are separated and $G_1, G_2$ are also separated is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module