If 4 integers are to be selected from {1,2,3,......20} such that the sum of the integers should be the multiple of 4, then number of ways to select the numbers are
A
1220
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
1120
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1200
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
970
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A1220 Every integer in the set is of the form (4p,4p+1,4p+2,4p+3) We can either select 4 integers of the same type say 4p then no. of ways are = 204C4 same is possible for every type no. of ways = 4(204C4)=4(5C4)=20
anothers ways is to select two integers of 4p type and two integers of (4p+2) type then no. of ways are = 5C2×5C2=(5C2)2=100 and to select two integers of (4p+1) type and two integers of (4p+3) type no. of ways are = 5C2×5C2=(5C2)2=100
One more way is to select two integers of 4p type and one integer of (4p+1) type and one integer of (4p+3) then no. of ways are = 5C2×5C1×5C1=250 Also to select two integers of (4p+2) type and one integer of (4p+1) type and one integer of (4p+3) no. of ways are = 5C2×5C1×5C1=250 Also to select two integers of (4p+3) type and one integer of (4p) type and one integer of (4p+2) no. of ways are = 5C2×5C1×5C1=250 Also to select two integers of (4p+1) type and one integer of (4p+2) type and one integer of (4p) no. of ways are = 5C2×5C1×5C1=250 So total no. of ways are = 20+100+100+250+250+250+250=1220